When a hose is attached to the outside faucet and the water is turned on, water spews and runs from under the light grey plastic cap on top of the faucet. The cap has "Antisiphon" on it and from what I understand, this plastic cap is a part of the vacuum breaker. When I try to remove the cap, it just turns and does not loosen.

Do I need to shut off the main water supply to replace the vacuum breaker poppet and cap or having the facuet on off be OK for repair?

I purchased a universal repair kit at Menards, would this repair kit stop the leak?

When I remove the water holes from the facet, no water leaks from current cap, its only when I attach the waterhose does the leak begin... Pressure related?

Any thoughts?

The anti-siphon device allows water to exit the faucet only, If the city water is shut off, water from your hose is not supposed to go back to the Citys supply.
Should be replaced.
A friend of mine once filled their waterbed, then shut the faucet off, Not realizing, The valve proceeded to empty waterbed out the anti-siphon device and on to the ground.
It was working perfectly.
If you turn faucet on and it doesn't leak out, then when you turn faucet off, and water leaks out, It is doing is job. The spray nozzle is holding pressure.