How do you rank-up your Chocobo Companion faster?

[Hairspray]

This is flat out wrong. When you take your chocobo companion out and kill mobs you'll notice a second xp text show up for each enemy killed, this is for your companion.

Yes I'm aware they have the 2nd exp total under mine... but since their "level" is identical to mine... it's really the "Rank" I'm concerned with, not the level... so I wasn't sure if that exp was what moves the progress bar or not.