[Confused and can't find help within Guides]

THANK YOU!

[Confused and can't find help within Guides]

Currently trying to raise a Rati and I'm at the final step of balancing stats.  So I transferred the MAG to my main who is Hucast Oran.  The MAG automatically changed from Ila to a Garuda, but when I gave back to my Hunewearl Yellowboze it changed back to Ila.  Is this a bug or normal and can I continue to raise the MAG on my main and give it to a A Type Hunter for the final evolution level?  I'm just trying to not shoot myself in the foot here, already invested a lot of time into this MAG.  Thanks for any help.