Dream Drop Distance Question about learning commands from Dream Eaters

Does it really matter who is "raising" the dream eater? Do some Dream eaters give new moves to Sora only when Sora is training it? (same thing applies for Riku) I've been training different teams for each Sora and Riku just so I can train them a bit evenly.

 

The inventory is shared, the only thing unique to each character is the abilities

 

So that means I shouldn't just have the dream eater be trained by only one of them?

 

Commands you unlock go into a pool that both characters can take from (unless they are exclusive to the character, like Ars Arcanum or Dark Break). I think the only thing this doesn't apply to is Keyblades, but I may be wrong. If you're trying to max out the Dream Eater's affinity it's best to have both Sora and Riku using the same Dream Eaters, but if you're just trying to unlock commands and abilities it doesn't matter.