Nope. Not normal.
You can test the thermostat in a pot of boiling water on the kitchen stove. Use a thermometer and see what temp the water is at when the thermostat opens. Personally, I would never install a thermostat that I didn't test first.
Parts store thermostats are junk now days. I have a 192* Calorstat in my truck currently, from RockAuto. Its been in for about 4-5 months and so far, so good. Typically, I would only use OEM, but I wanted to try the Calorstat since they're new to the US market.
Did you remove the plug in the top / front of the water pump when you filled the radiator? My normal procedure on the Hemi is to remove that plug, fill radiator until coolant drools out of the hole, then put the plug back in.
Then I put the radiator cap on, start the engine and while its idling sqeeze the upper radiator hose over and over. Usually with a few pumps of the upper hose, the hose will suddenly collapse. Then I remove the radiator cap and top it off.