Its interesting that you get differing advice from coaches about the serve motion. I actually asked Brett Clark the question about tightening up the fingers on ball contact 2 days ago and he said 50% of top coaches say to do this and 50% of top coaches say to be relaxed.
There is also Mats advice about using your wrist which I think implies using your wrist muscles vs Brett Clark's method to stop the forearm movement to let the wrist flick through being relaxed. If you shadow swing Mats method I think you can not get the shake at the end of the swing. I get a higher wrist movement speed from Brett's method. I could be misunderstanding Mats advice though.
I have actually tried to return Bretts serve as he was my coach and they are very deceptive and have a huge degree of spin.
There is also Mats advice about using your wrist which I think implies using your wrist muscles... I get a higher wrist movement speed from Brett's method.
This would make one think more deeply about what is going on and how to do it, (That thought provoking is good) Brett advocates allowing wrist to keep going after stopping the lower arm. I believe that to be biomechanically sound. If Brett is not trying to accelerate the wrist further, then he is keeping forearm loose and not using the forearm muscles. It would give him an option to firm up at impact if he wanted and he surely has a fast bat already. That is a big time important thing - you need a fast bat at impact to make big spin. Going back to the forearm muscles... if Brett is not using them to make wrist go faster, that would make it easier and more consistent to get your fast bat. You would be controlling the bat speed it with your lower arm snap and stop/slowdown to let the wrist get to speed. This can be consistent when learned and that is important.
Both Matt and Brett move the upper and lower arm to position, use a short area whip to accelerate the lower arm and stop/slow it down. Matt looks like he is accelerating the wrist. This can be practiced and controlled to be consistent and have a fast bat at impact. I believe Matt is also very loose in forearm and engages only at the right time.
A big error a lot of macho man type dudes do is to tighten up early... in arm, in shoulder and it destroys control and result. Besides bat angle too open to result in too solid contact, being too tight before impact has rekt many a player's serves to go long and get killed. Almost a suicide mission.
Brett explains things in easy to understand concepts and provides effective adjustments in his advice. This is useful to any level of player. There are many players who watched dozens of serve vids without much result, but greatly improved after trying out the things Brett advocates. That is a sign of effective adult coaching.
Matt really broke down all the relevant and important aspects and phases of the serve logically and compartmented. This is hugely important to adult learners as we need to know how and why.
My personal FH pendulum short under and side/under serves use less waist than both Brett and Matt. I have a hard time timing it all, so I use less waist rotation. That would make it harder to sell the serve like they do. I sell it with a fast bat and smooth motion, so it would be harder to pickup on my variation. My biomechanic of the whip are similar to both Matt and Brett before wrist. As for the finishing, I am prolly closer to Matt's way than Brett's. I try to accelerate the wrist some. I probably use a little less wrist than Brett. Why? I am not as practiced and good as he is. I play it safer.
Another thing is point of impact on the bat. A lot of players advocate to try to impact closer to the tip where the bat moves faster. On paper, this is good, but when you are boots on ground, it is a whole new world of pain when you start missing serves trying to impact the ball on that magical last two inches of the bat zone. Werner Schlager discussed that on a vi way back in the day and confessed that he does not attempt to use the tip of bat - he said he wasn't consistent enough and he can simply get by impacting it more consistently lower (more towards sweet spot of bat) and worry about how to make a fast bat - which is what counts.