Background Check Timing Summer Start

I summered as an associate this year. Accepted the return offer #1 but received a better offer #2 a few weeks after the deadline. I had a background check for the summer and passed. I have a misdemeanor dui that is “set aside”, the equivalent to expunged for certain states. Some what of a concern as different banks could react differently to the misdemeanor.

Wondering the timing of the background check for offer #2 if my start date is summer 2020. Want to renege ASAP on #1 out of respect but not before I am 100% about my offer #2 employment eligibility. Any insight into background check dates for summer starts would be appreciated.