Couple things...

One... the pink wire should only have voltage when the momentary button is pushed. Simply arming the system shouldn't do anything...

UNLESS... you have the pink wire accidentally wired to the wrong side of the button.

OR...

The momentary button is normally closed, and the sputtering you're getting is actually the nitrous turning on at idle.

Put a timing light on it. Have someone flip the switch, and see if the timing moves.

My bet is that it won't... I think you may have the nitrous turning on accident.