Accepted to PhD program but my graduation may be delayed until August?

[Curious questioner]

Hi.  I applied to PhD programs based on my belief I would graduate with my Master's degree in May 2019.  I have been accepted to start one PhD program (with an assistantship) in the fall 2019 and anticipate hearing from 3 other programs soon.  However, I now fear that I won't hit the thesis/defense deadlines at my university to graduate in May and my graduation will be delayed until August 1. Assuming that goes as planned, I will graduate before the orientation and enrollment dates in mid-August for the fall 2019 program.  I know I ultimately will need to notify the program that I accept, to tell them of this change, but, does anybody know if a delayed graduation date (which would still be before orientation/enrollment for fall 2019) is likely to change my acceptance (or assistantship!) in the program(s)?  I'm freaked out about this, so thanks for any thoughts or similar experiences.

Edited February 24, 2019 by Curious questioner
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[PsyDuck90]

You would have to talk to the program directly to get the best answer. However, as long as you are graduating before the start of the fall term, it shouldn't be an issue, as you are not delaying your acceptance. 

[zjppdozen]

If you are not an international student, it does not matter if your degree can be conferred before the start of your Ph.D. program.

If you are an international student, you should advise your international advisor to release your SEVIS ID as soon as possible after your degree have been conferred because your new school can issue you a new I-20 as long as they have received your SEVIS ID.