1098-T Box 1 less than actually paid?

(Hope I can tell this story clearly! All numbers below rounded for simplicity). In the past for each of my children, I had made 2 college tuition payments per year, about $25,000 each for each upcoming semester (one in the summer, one as soon as the bill was produced mid-December for the following spring semester) with withdrawals from a 529 plan. For my daughter’s final semester, spring 2022, the $25,000 bill was due January 16, 2022, I paid on January 6 (I'm now retired with little income, so hoped that paying in 2022 would have tax advantages, and we'd never before claimed any credit such as AOTC). I expected to see this payment reflected on 1098-T Box 1, but instead was puzzled to see only $9000. I noticed that my 2021 1098-T indicated $50,000, but I did not pay that – I only made 1 payment of 25,000 in 2021 because I made the payment for spring 2022 in January. I spoke to someone in the university who said things I didn’t understand, including how my Box 1 amount was “capped” by payments made in previous years and they can ascribe payments to when invoices are produced rather than when they're due or paid. I mentioned that everything I can find online seems to indicate that 1098-T should reflect when payments were validly made.

Anyway, when I enter into TurboTax the 1098-T info, with the $9000 that appears in Box 1, my tax is much higher than it would have been had the value been $25,000 as I expected. But in TurboTax there’s an optional field that says “Enter the tuition paid”, describing that this includes all sources, and if I include the amount I paid in that field the tax is much lower, around what I had expected, including obtaining the AOTC.

Whew! I guess my question is: Was it allowable for the university to indicate amounts on 1098-T that were different from what I actually paid in those years (much higher in 2021, much lower in 2022)? And does the “Enter the tuition paid” field in TurboTax address this correctly and adequately? Or anything else I should be thinking about? Thank you!