sounds like a positioning issue of the mech to me (check out park tools website for that).
Unless of course it's the wrong mech and always was.
Was this mech originally specced on that particular bike or was it added by someone?
If added have you checked the shimano specs for it?
If the mech was fitted after the bike was born may be an idea to tell us what the mech is and what the 3 chainrings are.
Also, could someone have changed the bottom bracket to the wrong spindle length for the chainset?
Congratulations for using a triple - nothing wrong with them - many advantages.
If it's a flat bar bike (better in my humble opinion) minor issues can be sorted with trimmable rapidfire shifters.