Can someone explain what Tommy is doing in the thumb flexibility exercise? Or if there is any other tips or exercises to help me get more thumb flexibility?
Tommy is pressing the E string with his thumb (all time on the same fret) while the other fingers are playing a chord progression.
Hope this helps… 
Thumb held on low E string fret 7.
He says you play an E- bass pumping.
Then I think he says you play an E-chord. But then he dances it step wise up and down by a semitone.
Does he mean an E-shape mini-barre - such as you have a mini-barre down at fret 1 for a smaller way of playing F?
I’m not sure if it’s an actual E chord or E shaped chord, I might just have to transcribe it.