The validity of the prayer depends on how it is done, not on when at least if you've started it within the prescribed time span. In more exact words if you've completed one full raka'a before the adhan started you are fine
As there are some differences of opinion on the correct beginning of the time of 'Asr among sunni scholars this could be a kind of issue in case of the 'Asr time according the hanafi maddhab which usually is later than that of other schools of thought, but where's a difference of opinion there could not be an agreement and therefore this still isn't a reason for declaring a prayer void.
I'm pretty sure that there are enough answers on this site explaining the details.