Your question appears to me to be entirely appropriate for this site. Mottos and dedications (and tattoos) are regularly featured here.
That said, your phrase is not correct, as the adjective you're looking for is splendidus, -a, -um and not splendidis. It should therefore be:
Splendida mens mea
(You asked if your proposal was “a proper construction.” Well, technically it is. It is a bit of a habit of Latin fans to figure out theoretically feasible meanings for everything, and you could read splendidis mens mea as “my mind for brilliant people” or something like that. It is much more plausible that someone thought the adjective was splendidis, -e.)
It does then mean what you suppose it means, although I find it puzzling why someone would put that on a graduation gift. I do not immediately see any reason why the construction would be different for a teacher. (Mea does not depend on the gender of the speaker, in case you are suspecting something like that – that can happen in Latin, but not here. It does depend on the number, if referring to several people you would write nostra instead. You could also write nostra in case of a single person, but that's another story.)