In the movie, Alice through the looking glass, when Alice was running from Time in the past, she uses glass to run away; So why didn't Time use the same to catch her?
Could only Alice use the mirror to move? Or was the glass magical?
Alice never used "looking glass" to run away from Time, she uses Chronosphere. Looking Glass (mirror), like Rabbit Hole in Alice in Wonderland, is simply a portal between real world and fantasy/imagination. In the movie, Alice Through the Looking Glass, it can be seen many times how Alice steps, falls and switches between real and fantasy world.
Well as it is Alice imagination, then I think the right answer would be - Yes, its only for Alice. Time did not use it, because HE does not exist in real world. Alice never used looking glass to to get away from Time or any other Character in Wonderland, its only a symbolic portal between real and fantasy world. Also as it appears in the movie, it was never deliberate choice, but more of accidental-curiosity-escape scenario that draw him into the looking glass (rabbit hole).
On screen the use of mirror offers clear and understandable distinction between real world and Alice world to viewers.
For me much more eligible question should be, why Carroll used looking-glass symbolism? But this has been asked-answered in many sites and its roots come from culture folklore.