I have verified the theory that this large initial progress is what has been earned in the match, and no, it's not. After the game I have assigned all training points, then initiated the training, and saw the effect of warm-up in the ballpark of 13-15%. On subsequent training, it dropped to 2-3 and then to 0.

Another effect I also noticed is that there's no obvious correlation between particular training being "very easy" or "very hard" (with everything in between) and gained percentage of skills. One would expect that hard training will bring more skills in return for larger drop of players' condition, but it does not happen.