Matric means "matriculated".
Matriculation is your formal admission as a member of your COLLEGE, which is what happens when you "go up" and the beginning of your studies.
You do not actually become a member of the UNIVERSITY until you graduate and "go down", at the end of your studies ... and I'm guessing (don't know for sure, because they do some things in pretty queer ways at Oxford) that "admon" is "admission" ... to the university, upon graduation.