Thumbs on mittens

Hi guys i’m working on the pattern from knitty for fluffy cuff mittens,

I think I may be overthinking this already, but i’m about to start the thumb, and I understand that after you mark the thumb area, and you go all the way up to the top,

Q. "Do you bind off the mitten, cut yarn and then go back to the thumb? or is it still attached (yarn) and then go back and work on the thumb??

I looked at the video on DYI but i’m still a bit confused.

You put the thumb stitches on hold, finish the rest of the mitten, cut the yarn and then do the thumb.