You use UMD to act like you have a caster level of 30 to activate the staff, however, the staff does not use that CL 30. It only activates with it. Let me try at an analogy.
There is a Magical Chalice which turns normal water into Holy Water if someone turns undead within 30ft of it. You can UMD to pretend like you turned undead, thus gaining Holy Water. However, undead around you are not turned.
You act as if you have the class feature ONLY for item activation, not item use.