First of all, thank you all for your contributions to the discussion. The critique and praise both have been a good read, but now after the first training has run (and in the future after more trainings do too) you'll have a better feel for the real effect of the new staff. I'll wait for that to happen, keep an eye on the discussion here and, as I said, up the feature "denomination" from minor to major.
Some more specific answers follow:
@khenry: The boost is only applied to players playing at the correct training positions and if they are 18 or 19 yo.
@LA-King Leonidas: You're right, the hire button should be visible until you have all 6 covered. Made the change now.
@Bass: I can see both the main trainer and the youth trainer. Is there still a bug?
@mark lenders: Yeah they stack but their combined effect is reduced.
@barba & kingK: this is just a display bug, you're not supposed to be able to hire internally the secondary staff. If you clicked the button you'd notice that only the essential staff members can be hired internally.
@Ubiond: fixed the specialty issue now.
@ychonodou: youth trainer just boosts the training of 3 players trained as long as they are 18 or 19 years old and as for the sports psychologist - it is for the ones who did not manage the minutes well or a random factor would bring the GS down (so he stays at level 9 if maxed).