Mystic is actually probably a good call.
Like the other base D&D classes we need a "real" word, that actually is somewhat evocative to mainstream culture. Everything in the PHB make some degree of sense to just about everyone. Psion(icist) doesn't do that (regardless of how you feel regarding any potential sci-fi tones to the term).
Now, the classes in D&D of course have their own take on the term that you have to be familiar with D&D to truly understand.
When non-D&Ders hear class names...
Barbarian: Might be Conan, but also might be non-Greek-speaking peoples in antiquity, or someone with atrocious table manners.
Bard: Could be a minstrel, might be Shakespeare
Cleric: Not someone in armor calling down miracles
Fighter: Full-contact fighting sports--not soldiers or mercenaries
Monk: A monastic religious devotee, whether western or eastern. The immediate connection "monk = martial artist" is pretty much D&D derived. Shaolin monks don't define the word "monk" for very many people.
Ranger: Park ranger
Rogue: Sometimes a scoundrel, often someone who "went rogue" in any of a variety of contexts. Almost never a thief or assassin.
Sorcerer: Generally a vague term for a "magic-user" of some sort, sometimes with sinister connotations
Warlock: A devil-worshiping "magic-user"
Wizard: A "magic-user" of some sort
Druid and Paladin (outside of D&D inspired fiction the term is extremely obscure) are probably the ones people are least likely to have alternate meanings come to mind for.
So basically, the names work about as well as could be expected. A non-gamer isn't necessarily going to get exactly what they are, though some of them might evoke the correct D&D meaning. Once it is explained to them it doesn't seem too terribly off. Rarely do you hear, "How in the world could you interpret sorcerer as some sort of high-powered magical sort, rather than as a diviner?" But some of them (such as monk, cleric, or rogue) might very well elicit a "huh?" response. It's a mixed bag, but about as effective as can be expected.
So let's look at...
Mystic: You get everything from someone generally associated with the occult in any sort of way, to a religious devotee whose practices emphasize direct experience with the divine, to a New-Ager, to a palm-reader, to however someone's particular fiction of choice happens to define it.
General conception of the meaning of mystic seems as close of a hit to the (proposed) 5e D&D meaning as a general conception of rogue or monk are to what they mean in D&D.
So it's definitely on the lower side general concept to D&D correspondence. But...what other suggestions do we have that...
1) Don't invoke sci-fi themes for many people (Psion)
2) Don't sound like an adjective more than a noun (Psychic)
3) Aren't too modern or specific sounding (Mentalist, Telepath)
4) Aren't made up terms that mean nothing outside of specific fictional contexts (Esper, etc)
I'm pretty sure that the designers are thinking about those sorts of considerations.