Which "Character Quest" feats can be completed in the Marquee event?

Title says it all, while doing the marquee event, there are some feats that can be completed simply by doing a marquee battle as you can see all of the pop-ups showing progress when you finish doing a marquee battle.  

But then there are some that just don't count and you need to do a battle in a different game mode.

In the current marquee, the "Win 5, Win 10, Win 20" with Batcher don't seem to count even though you are using your own Batcher in all battles beyond T1.  Same with the "Win with Batcher and Omega (F)".  You are using your own Omega in these battles, but i had to do a battle outside of the marquee to complete it.

So, if this is by design, please provide some indication as to how we know which feats can or can't be done in the marquee event.  And if this is a bug, please fix it.