I just assembled my engine and have been adjusting the valves but there is a strange thing happening. The drivers side stays the same but the rocker arms have some slight "snap" when I pull the arm after adjustment.

The drivers side keeps tigtening up again after I rotate the crank thru the complete cycle. Is this normal on a new rebuild or does this indicate something else?

If it tightens up, you could assume the valve springs are pulling the head of the valve thru the seat, the valves on that side are sticking in the guides due to insufficient clearance, the pushrods are not seated correctly or you are not adjusting the valve lash on the heel of the cam. Those are the choices I would be looking at.

#1 doesn't sound feasible on a "new" engine
#2 is very plausible
#3 is remote
$4 is very plausible

Good luck!

OK...I checked that the rods are seated and then made sure the rocker arms were pressed down completely against the cam before rechecking the clearance and it's the same now. Should I assume since I only have assembly lube and no oil at this point that the arms are just sticking?

go to the one side of the engine. turn engine until one of the exhasut valves are completely open. then go DIRECTLY across motor and adjust that exhaust valve, continue on with intakes etc.

Sounds like you are adjusting the valves when they are not fully closed.