AtTiny85 Reset Pin troubleshooting
333 &Omega; base resistor!?

I haven't really read all the rest of the question, but that's ridiculous for what you are trying to do.  The transistor is driving a 10 k&Omega; load, which is reasonable.  Even with a 10 k&Omega; base resistor you're barely asking the transistor for any gain.

Change R2 to 10 k&Omega; and see what happens.  This may have nothing to do with your symptom, but it should be fixed anyway.  You haven't specified what this "NI" thing is (did you get that from Monty Python?), but maybe it isn't reacting well when one of its outputs is held low by 333 &Omega; to a 700 mV source.