Hi,
"2 under" can cause your average to go up or down depending on where your average is and what course you are playing.
In your last game at St Andrews, par is 72 or 36 for your 9 hole round. Your 34 (2 under) works out to an 18 hole 68 (34x2), which counts toward your average and will increase it, if you had a 66 prior to the round.
This will all become moot in your next round as a master (congratulations by the way!): Your first round as a master resets everything (average as tour pro is tossed out), so your new master round result will launch a brand new average for you.
Keep doing what you're doing (ranked stroke play rounds/tournaments) and practice at your new tees to lower your score. At master level, this will be a bit more challenging, and many consider trying better performing equipment... or not. Enjoy the new views :)
-Keith
EDIT: have not checked if you are saturated at tour pro level, but if your average went up you probably didn't... you earned your new tier by playing tourneys