Huge experience boost

[Psitticine]

You've got it right. A unit will get a "red star" skill once it enters the Hall of Fame. The skill will continue to improve as long as the unit is still in the Hall of Fame (even if it is dead) If the unit is booted from the Hall of Fame by the progress of other units, they do not lose the ability. It merely ceases to improve until the unit is again in the Hall of Fame.

I'd guess what you're seeing is the product of that "turn over". Your units are making the list, probably at the lowest position, and gaining the abilities. They then get "bumped' off the list by another up-and-coming unit and so have the ability but are no longer on the list.