Generally speaking, you have to tell the bank when you make a deposit, whether it is for the previous year or current year. I always make electronic transfers and there is a drop-down menu to select which kind of deposit I am making.
If you mailed a check, and the bank assigned it to the wrong year, it is up to the bank to correct the record. There is nothing in the tax code that says they can't, but there is nothing in the tax code that says they must, unless it is clearly their error. They would have to issue a corrected form 5498-SA to you as well.
For the bank to make the change, they would have to accept responsibility that it was their mistake to credit the deposit to 2018 (or at least agree that the instructions were ambiguous). Whether or not they do that is up to them. Also, from your mistake in February, you had 2 more months where you could have corrected the mistake before April 15, if you checked your account online. They may be reluctant to make the change now.
I suppose the bank is reluctant because, if they allowed illegitimate recharacterization, or were found on audit to have lax controls and procedures, they could get penalized. (That is, if a customer makes a deposit in March 2018 that they plan for 2018, then discover in September that they have extra money and could contribute more in 2018 if they retroactively change the other contribution to 2017, that should not be allowed, and a bank could get penalized if they have poor controls and accountability.)
