Lol! When I first started really listening to Dexter, it was like the voice of God. Well, if he played some of the greatest tenor I ever heard...he was such a master of expression, drama, excitement... one of the most engaging soloists ever.
It's mostly an alternate fingering thing. Not much to do with embouchure at all, beyond his normal great air control. As pointed out above, he's going between the 'normal' A fingering and the alternate A (XXO/OOO and XXO/XXX). He's also hitting a G or G# in there. Experiment between the two fingerings for A, and hitting a G or G# and you'll get it. It's not particularly difficult. Certainly not as difficult as getting his entire concept/sound going!
This, but add low C to get that 'whole horn' honk on the alternate A. Usually you open your throat during passages like this, as in a lip trill on A2 or Bb2, and those require the same alternate fingerings to get more of the horn into it so the definite note change in the lip trill works. You can do the same 'ooba doobah' on G2 except you have to keep RH 1 &2 up. Now, here's a very arcane bit for you that I wouldn't know unless I had been figuring out rock and blues licks all my life; during the 'ooba doobah' passage, you can also slide your tongue over the beak of the mouthpiece at a different rhythm than your fingers are moving. Now Dex didn't do this but plenty of others did/do. In fact, you can use this method in lieu of the alternate fingering because it cuts the sound in half, giving a similar (but different) effect. What it does not give is the 'whole-horn honk' on the alternate side of the figure.
