SWTOR is a bit funny with it's group ordering, but normally the issue is you need to get the Select keys working correctly, i.e. the F1 to F6 select party member assignments.
Once it is sorted for a given team, as long as you log in the correct toon into the correct slot, then it should be fine.
Lax covers SWTOR in this video...
https://youtu.be/VPc9pBj-47kHe goes on to explain the party member select in this section of the video..
https://youtu.be/VPc9pBj-47k?t=232And then at this point he covers setting the in game binds, and working out the ordering needed for the F1 to F6 party member select keys,
https://youtu.be/VPc9pBj-47k?t=680