The employer (you) not the financial institution is the one responsible for tracking the year for which a SEP contribution is made. The financial institution only tracks the year in which a SEP contribution is made, not the year for which the contribution is made. If you want your SEP contribution that you deposited sometime between January 1, 2022 and April 18, 2023 to be your SEP contribution for 2022, you simply report it on your 2022 tax return and not on your 2023 tax return. You seem to be saying that you have already done this, so everything is fine.
(JulieS's answer is incorrect because it indicates that the financial institution is needs to know the year for which the contribution is made. The financial institution does not need to know this, nor would they do anything with that information if you gave it to them. The need to know the year for which an IRA contribution is made only applies to regular personal traditional or Roth IRA contributions, not to contributions to IRA-based employer plans.)
