The open ended hose is for winterizing... You turn the valve and it sucks yucky pink stuff out of the jug.. I used air myself, saves on the pink yuck.
The pulsating you cite is normal.. For example. If I open my kitchen faucet on HOT.. the pump can pump more than the faucet can pass as the pressure increases it shuts off and decreases turns back on... (MIXED hot and cold does not do this)
The solution is not an adjustment it's a new variable speed pump.. or at least I think it is.. this is aq pump that speeds up or slows down as needed. to supply just ENOUGH water. Or so the ad suggests.
Not having one I can not be sure .