It depends on which train you've booked. Some Amtrak trains terminate in NY, while others run through to Boston and stop in Stamford along the way. I'm assuming and hoping that you're booked on one of the through trains.
Flying into EWR over xmas, going to STM-do I change trains or am I good to go leaving EWR?
You might save some time if you take the #62 bus to Newark Penn Station, rather than the AirTrain to EWR Rail Station. More Amtrak trains stop at NWK than at EWR. But if you're traveling on a combined Continental/Amtrak through-ticket to STM, that option might be a little problematic.