I have a bladder type water tank with the pump mounted on top of the tank. There is one water line coming out of the bottom of the tank. It appears as though the line from the pump has a “T” and a line connects to the bottom of the tanknd the other outlet from the “T” is the water supply line.
That is correct. It wouldn’t hurt to have a check valve after the outlet of the pump. This will keep water from running backwards through the pump outlet if the pump is shut down.