There are cases where changing the Role and RemoteRole of a Pawn doesn't get properly replicated. The underlying issue has to do with ScopedRoleDowngrades and Shared Shadow State.
A workaround is to set the cvar net.ShareShadowState to 0, though this will likely negatively impact server performance.
*Note:* Order of client connection *is* important.
Excepted:
Only the currently possessed pawn has Role AutonomousProxy on the second Client, all other pawns are SimulatedProxy.
Actual:
Any pawn that was ever possessed by the second Client has Role AutonomousProxy.
There's no existing public thread on this issue, so head over to Questions & Answers just mention UE-54477 in the post.