Heating the material to straighten it is a temporary solution. Sealing all sides of a project does help considerably regarding moisture absorption but supplies no help in seasonal heat expansion regardless of a ply/lam mat or solid wood.
Regarding the 2nd video, I would have kerf cut the flat sawn wood on the inside of the ring pattern as opposed to the outer. The number of kerf cuts would depend on my method of fastening the mat to the project. In all the remods I've been involved with, one thing I always found regarding door frames and thresholds the back and bottom sides were always kerf cut to prevent cupping. I also would not have cut as deep as the man in the video, that weakens the mat at the cut enough to possibly cause a split during a shrink stage.
Work smart not hard!
Never bite the hand that looks dirty