Concern about Promotion Representation in Resume

So, this is a bit tricky. Since COVID was a time for extreme work overload and not enough employees to handle in the marketing agency world, in April 2021 I was told by my Manager and VP (after a year of working with the company) that I will be promoted to a Senior role in May 2021. This meant I will have 2x brands under me, a couple of juniors I had to train and of course be the lead SPOC with clients. From May 2021 onwards, I was introduced as a sr. strat to all the clients, my email signature had the designation and the team was structured basis that.

I was told, that my appraisal + promotional arrears and money will come in, September onwards, due to slow downs in financial processes during COVID.

Now, to ensure there are no issues in future BG checks in case I get admitted into a B school, I was checking my Payslips. I saw that the payslip only mentioned the senior role September onwards and not May onwards. So I am guessing - if the verification team reaches out to an HR they will simply look at the payslip for confirmation of dates.
However, all my supervisors and upper management would agree that I was a senior from May onwards.

Should this be clarified in my resume, or in some place else? (the vp is also my recommender)