When I hear "time crystal", I think "the wielder of this object can travel through time, or at least do something far out, like see past events", not "a crystal that when vibrated breaks symmetry".
And whenever I hear time crystal, I think of bad sci-fantasy 80s movies.
“Mondor, you must grab the time crystal before the second moon equinox, or the Flarborg will be released from their electronic pen and ravage us like they’ve never ravaged before!”
I believe the most recent iteration of star trek is particularly guilty of stealing "time crystals" from the science news headlines and applying it to this sci-fi trope.