Is the 'Asr prayer that I performed in congregation after the Maghrib call to prayer considered a qada' (make-up) or ada' (on-time) prayer, knowing that the congregation had already begun their prayer before the 'Asr time had expired?

The adhan heard after sunset signals the departure of Asr prayer's time, making the prayer a qada' (performed after its prescribed time). Performing a prayer, either in whole or in part, within its prescribed time is considered ada' (on-time performance), whereas performing it after its time has elapsed is qada'. Your Asr prayer in this instance is qada' because it occurred outside its designated time. However, your joining a congregation performing Asr as ada' is permissible according to some scholars, such as the Shafi'is, and you are not required to repeat the prayer.