Another thing I have noted: always have your pet in "heel" before starting and Primal...

I think I had left her on "Place" during an Ifrit fight then started Garuda on DF...
We were still in the forcefield at start (while someone watched cutscene) that Garuda was already attacking us...
And I could see my fairy over there, near where Garuda usually stands...

She also fly away if she was on "place" before you used Return (like in CM for instance)

They should really put an auto-heel when teleporting/returning or leaving and Instance