The picture you have attached has a built-in vacuum breaker, but your comment says you "just screwing it in tightly".
If it's a standard non-freeze hydrant with a screw on vacuum breaker. the vacuum breaker would not leak as it is just a check valve to stop water going back into the wall hydrant from the garden hose.
I would think it is not seating properly. The problem with a wall-hydrant is you cannot replace the cartridge like you would normally do in a faucet as the seat is at the bottom. You would need to replace the whole unit.