You can use Grey pipe underground.
Grey Pipe can be above ground or underground without any issues.
Plumbers use purple primer on PVC as it cleans the pipes and fittings of dirt, oil, grease or other foreign matter that can make it difficult for the PVC cement to bond the fitting and pipe together.
The Purple primer when used on PVC pipe also softens the plastic of the pipe so that it bonds together easier as well.
Before turning on the water you should allow the PVC glue to dry and cure for at least 2 hours.
It takes at least 15 minutes for the PVC glue to get a good bond with the pipe and fittings but for full strength it takes up to 2 hours.
So you should always wait until 2 hours have passed before you pressurize the water system and turn the water on because turning the water on too soon could cause the pipes and fittings to come apart.
The PVC glue melts the pipe and fittings together through a chemical reaction.
It does not glue the pipe like normal glue but instead melts the pipes together to form the bond and it can take 2 hours for the reaction to fully work and create a good permanent strong bond.
Also when putting the pipe and fittings together make sure to twist the pipes and fittings back and forth and hold them together for about a minute.
Holding the pipe and fittings together helps keep the pipes and fittings from pushing apart.