No Limitations Specified in the text.
Ioun Stone, Reserve (DMG p. 177)
Any creature can cast a spell into the stone by touching it while the
spell is cast.
Once that spell is cast into the stone, it is waiting to be released by whomever has the stone. ("You" in the text of the description." No class or level limitation is noted, so no specific to overrule the general. That means that a non-spell caster, whomever has the stone, could cast a spell. (For example, the bar maid whom your Warlock favors ...)
You can cast any spell stored in it.
No class or level limitation in the text. That means that you (you=the one with the stone) can cast any spell. (When the barmaid casts the fireball, won't those ruffians be surprised!)
... is otherwise treated as if you cast the spell. (DMG p. 177)
Since all characters have Constitution, and concentration checks are based on Constitution, then if you need to make a concentration check, use your Constitution.
... you must make a Constitution saving throw to maintain your
concentration. The DC equals 10, or half the damage you take.
(PHB p. 203)