Party member placement is not updated correctly from PHS - and not at all from the Order screen. I don't know if that's the case in PSX.
Cloud
Tifa
Barrett
Cloud has ID 0
Tifa has ID 2
Barrett has ID 1.
The vars (Bank 2 [9], Bank 2 [10] and Bank 2 [11]) should hold the following:
0
2
1
Which they will be if you use PHS and completely change the party. But if you swap the characters about in the order screen, the vars will remain 0,2,1. So if you then have this order:
Cloud
Barrett
Tifa
The vars will still be 0,2,1. At cutscenes, this means that the game will behave as though Tifa is party member 2 and not party member 3. The PHS menu also suffers with a problem. If you completely change the party, the vars will be updated properly. But if you swap out only one member, the vars are not updated properly either. So the cutscenes will again display members out of place.
The vars Bank 2 [9], Bank 2 [10] and Bank 2 [11] are ALWAYS supposed to mirror 4F8, 4F9 and 4FA of the savemap (which are updated with Order option also). At the moment, this is not happening. I should be able to add this fix for R06.
edit.
Because Cloud can be moved in the order screen, it messes this up. So the order screen not changing vars may be deliberate. Still, PHS is not updating properly when swapping out one char. That's definitely an issue.
edit 2.
Because the party leader isn't locked to the first slot, they've basically created some sort of crappy update procedure to make sure the party leader doesn't end up being placed in the vars reserved for member 2 and 3. What they should have done is lock party leader to the first slot.
edit 3.
An easy fix is to simply make party member 2 always equal the member that is highest (ignoring party member 1, who is leader). That way, if order is
Tifa (2)
Cloud (0)
Barrett (1)
Tifa will be member 2 and Barrett will be member 3.