I just went through something similar, I think, if I understand you right.

My brother came to visit and he wanted to play his account on my PS4, but the game did not let him change the Final Fantasy login to his, it was locked on my own.

The solution is for him to log off my PSN account and log into his own PSN account, then he was able to login with his own Final Fantasy account.

If all of you play with the same account, you wont ever be able to play at the same time from different machines in the future. If you ever want to play together, you will want individual accounts.