So, the video you posted was excellent (I certainly cannot make improve on the vid) so I can only describe what it feels like to execute the bind.
When you transition from the trapeze into an undermount the yoyo is set up for a bind. (the direction of the spin against the string-wrap around the axle).
When I was learning this bind, I had a tendency to throw the yoyo too high too fast. What I found to be effective (for me) was to toss the yoyo up (gently) and try to get it to apex at eye level. As it reaches eye level, I tug downward slightly with my throw hand (which is now directly below the yoyo). Then just catch.
Once I stopped throwing the yoyo to hard-quickly into the bind, I was able to use the undermount to transition to other binds as well. You’ll find that from an undermount you can not only do the vertical bind that your doing… but you can toss the yoyo down and to the side, or upward to 45 degree angles (either side). It’s neat because that one mechanic can drive many different (looking) binds.
I hope this info is helpful to you. Good Luck!