This happened to me as well, here's how I handled it:
School 1 - (interviews open for all) - After I completed my interview I found out about my new salary/role. I called the school to find out my options. They got me in touch with someone that would update my file. I was successfuly able to update my file, before decision time frame.
School 2 - (interview through invitation only) - My interview was scheduled to be in a few weeks after my new salary/role would take place. I decided to mention this in my interview at the end when they ask us if there is anything else we need to tell them. The interviewer jotted it down and told me they'll get it updated.
No school will require instant verification through a company letter or anything, because they will be verifying the info when you decide to matriculate anyways. You should try to update them through the interview or call the school if there is still time for the decision.