wa 'alaykumus-salam If you have completed your own 'asr prayer - you cannot join another prayer as being the same 'asr prayer. Normally if you join a jama'at of a prayer that you've already prayed you can do it as a nafl prayer, but after 'asr nafl is not permitted (makruh tahrimi). Therefore you should not join the jama'at.
assalamu alaikum, on a couple of occasions, i have read my prayer like asr on my own and then suddenly a jamaat starts in the same place. in such cases, at times i have just finished my salah and left and other times, have finished my salah and then repeated it with the jamaat, but im not sure if thats allowed or not?