I had this glitch happen a while ago with a Chocobo... during a fight with Ifrit too.
Basically the tank got on an invisible chocobo and rode over to Ifrit but when they dismounted they didn't on my screen so they stayed "mounted" on an invisible chocobo.
Entering the fight didn't help either. They were stuck at the entrance on their invisible chocobo so if I was near where the tank was (where they actually were, not where they were on my screen) I couldn't cast any spells on them because they were "too far" away on my screen so if I was still on CON I would have needed to camp at the entrance point to be able to heal the tank lol (luckily I'd just switched to LNC)
Just uploaded a screenshot