I don't think the hidden sing/magician/acrobat skills conform directly to their respective career levels. I say this because I've levelled both a singer and acrobat to a level 10 career, and whilst the singer could always pass her auditions to sing at the "Ultimate Venue", even as low as level 8, my level 10 acrobat still fails her auditions, because I think, she got most of her career levels from just leveling her athletic skill, and so I'm guessing (no way to check outside of mods) that her underlying acrobatic skill is still actually quite low.
If Master Controller an show the hidden skills as per Branr's post, then I'll take a peek with that and see if I can confirm this, or at least give a bit more weight to this theory.