Trait:

I FORMED THE BROTHERHOOD OF EVIL: Leadership. // Once per turn for all characters with this trait, The Brain may be given a non-FREE action after being carried, but only if he shares a keyword with the character that carried him.

Question:

Does this mean any time after being carried? It doesn't say immediately after resolutions, etc. I'd think I could do other actions before The Brain could do his non-FREE action after being carried. Am I correct in understanding this?

That would make the Brain proforma non-free action after what other action you assign and not after being carried.

Thank you.

I'm not 100% certain if Coyote's Own is suggesting that you must immediately take the non-free action with the Brain after being carried, but that would be incorrect.

The only relevant stipulation is that you may be given a non-free action after being carried. Nowhere does it say this must happen immediately. Other actions can be given between The Brain being carried and being given a non-free action.