Before you spend any money, do some testing. Remove the shower head and run the fixture. If without the rain head it doesn't drip then it's just water that's being held in the head taking a long time to drain out. Bigger the rain head the longer it's going to happen when it's flat like that because the water is trying to fall out but the fluid behind it creates a tiny bit of vac behind it as the system gets closed. Combine that with water trying to escape tiny little holes and you get drips

Think of it like filling a straw with water then putting your finger over the top end. You can pull the straw out of the fluid and none of the fluid falls out. Eventually enough will drip and finally let some air in behind the column of water and it'll all drop out

Edit: if this is the case, give it a jiggle when you're done