With apologies to Jay Kidwell (and you really ought to read his book, Instinctive Archery Insights, if you have a problem with target panic), target panic is caused by programming the brain to release the arrow as soon as we reach full draw and come on target. After releasing the arrow a number of times when we come on target, the brain develops a learned response, and begins releasing the arrow in anticipation of reaching full draw and coming on target, which is where the problems start. Kidwell's approach is to de-program the brain using various exercises, which have proven to be effective.
Linsin's "push release" is a method of turning the release into more of a mechanical process that is controlled by the conscious brain rather than just letting the subsconcious brain decide when it's time to release the arrow. The problem Linsin has to overcome is that we are taught that the release should be a surprise when it happens or you will ruin the shot. How can it be a surprise if you consciously decide when to "pull the trigger?" His solution to that problem, which is clever, is to use one of the holding fingers to "squeeze off a shot" in the same way a rifle shooter would, thus keeping the shot more under the control of the shooter, while also maintaining the surprise element of the exact timing of the release.
If you really want a comprehensive understanding of target panic, get Kidwell's book.
On the other hand, Linsin's method is not described in Kidwell's book, and I found that learning it gave me more confidence that I could control the timing of my release. Once I got that confidence, I did not decide to continue with his method as my normal release, but I think going through the process improved my shooting.
Linsin's DVD is reasonably priced, and I would not cheat him out of a part of his living by passing around free copies, other than to my immediate family and friends with whom I normally share things.