The FIA in turn was moved to remind the F1 CEO and everyone else that the regulations are the responsibility of the governing body and not the commercial rights holder.
That little exchange was further evidence that the cost cap is now an integral part of the way the championship functions, amid the inevitable innuendo in the paddock and suggestions that some teams may have gone over the limit last year.
After Red Bull was caught out for overspending in 2021, everyone now realises that a breach of the financial regulations is as serious as a technical and sporting transgression and that a heavy price can be paid, even if rivals felt that a fine and a cut in aero testing was not a harsh enough sanction for Red Bull.
Despite their initial reluctance, the teams now accept that the FIA can successfully police the cap. However, the biggest criticism of last year's process was the time that it took for that policing to take place, and for the results to filter through.
It wasn't until the Brazilian GP weekend in late October that the final outcome of the 2021 investigations emerged and Red Bull received a penalty, by which time the 2022 season was almost over.
That timing was not ideal, and Domenicali is keen to see the process move faster this time around.
"Control is in the hands of the FIA," he told Motorsport.com. "Personally what I have asked is to anticipate as soon as possible the publication of the investigations made by the staff of the FIA.
"But I say this only because, in this way, it does not give rise to speculation and comments that are not good for anyone."
The FIA accepts that the process could do with speeding up, while not compromising the level of detail that its investigations require.
Having learned some lessons, and bolstered its resources with an increased headcount, the governing body is confident that the outcome of the 2022 cap analysis – including any transgression and penalties – will indeed be revealed earlier than was the case last time.
The process started in the middle of last season when the teams had to hand in interim submissions by June 30. Those were projections of spending for the whole year to December, and as such represented a starting point for discussion, allowing the FIA to look for any potential issues.
The full details of the actual 2022 spending had to be submitted by March 31 this year, which is when the forensic examination of each team really began, including a series of factory visits.
"The first month after that deadline is dedicated to an in-depth review of the information submitted," says FIA single-seater financial regulations director Federico Lodi.
"And when we talk about submission it's not just a few spreadsheets. Each submission is composed of a 150-200 page document, so there is a lot of documentation to go through.
"The first month is usually dedicated to a detailed review of all the documentation to perhaps identify areas that require a little bit more in-depth analysis. We then identify follow-up questions and request more documentation, if needed, in preparation for our planned arrival at their facility.
"This is where we basically undertake an on-site audit and this usually starts at the beginning of May. And from then onwards we basically spend months on the road, visiting one team after another and basically rubber stamping their submission."
Given the scale of the operation it's not surprising that it takes time to dig through it all.
However, Lodi is well aware that the series as a whole can't wait as long as it did last year when confirmation of the Red Bull penalty came almost seven months after the final submissions.
"It's clear that there is an interest from the stakeholders to have a quick outcome," he says.
"We, as the FIA, understand these requirements, so we have strengthened the department, and now we have 10 full-time employees working on F1 financial regulation. This is a significant increase over last year, when it was just four.
"However, it is still clear that it's difficult to commit to a rigid timeline, as there are many variables that need to be taken into account. First, there are the findings themselves – what we identify and what we need to dig into further.
"On top of that, we also have to take into account the fact that we do the review with the support of the team, and obviously, the finance department of the team is also busy with running its business; they may also have a reporting commitment to their shareholders for example.
"So while we need to work as quickly as possible, for us the most important thing is not to undermine the robustness of the process."
Lodi acknowledges that it wasn't easy to recruit the right people for his expanded team.
"It's massively complicated. Everyone in our department is a former auditor. That's not a problem, the pool of auditors is quite large.
"The challenge is to find someone with a sporting background and then a motorsport background and finally knowledge of F1, because it is specific. We struggled initially, so we have decided to take another approach, and we are training them internally on the specificities of F1."
Aside from increasing the headcount, Lodi says the process will automatically speed up as both the FIA and the teams themselves become more used to what it involves, and how much detail is required.
"Simply, the more everyone becomes accustomed to the regulation, the more you become accustomed to the process, the more we are structured, clearly the time will be reduced," he notes.
"But we have to be realistic, because I don't think that it will be feasible to finalise the review after one month or 45 days. It also depends on the findings, because if you need to open a formal investigation, it takes time.
"There are lawyers involved, advisory boards, so the process is a long one. But we have a clear target in mind to do it quicker."
Last year's process saw everyone learn lessons, not least Red Bull, whose interpretation of certain elements of spending differed from that of the FIA.
It's no secret that this year the governing body has been digging deeper into the role of technology divisions that sit alongside race teams, with greater attention paid to how the time of some engineers is divided between the two.
"I think that in year one, there was a little bit of uncertainty, because it was the first time a financial regulation had been brought into professional motorsport," says Lodi.
"Also, I think that for the teams it was a little bit challenging, because the regulations are objectively complicated, because the businesses we have to regulate are complicated.
"When we are talking about organisations with 1000 employees, undertaking engineering activities, manufacturing activities, with commercial and racing arms. So the business is complicated.
"Now, after last year I am confident that the doubts everyone had last year are clarified. So hopefully, going forward, we will have less and less difference of interpretation in respect of the regulations. Even if they are still discussing how to interpret things on a weekly basis."
That dialogue in turn feeds back into rules, which are constantly subject to review. Most of the ongoing updates come in the form of clarifications that are the equivalent of FIA technical directives, and which are seen only by the teams and are not officially published.
Lodi notes that during the 2021 process, some teams asked more questions than others, and those who appeared to be more relaxed have been rather more vocal during the current investigations.
"Last year the numbers of clarification requests varied significantly from team to team," he says. "I think this is another lesson everyone learned from last year.
"What we have seen after last year is that now, almost all the teams are very forthcoming and are now trying to discuss with us any doubts they have beforehand. This is another aspect that will hopefully reduce the risk of misunderstanding."
So were there any transgressions in 2022 and will serious penalties result? Hopefully, for the sake of the championship, we will find out sooner rather than later.