The compressor cycles normally (on and off) and the cycles can be pretty short, way less than a minute.
The Aux fan comes on as soon as the compressor clutch cycles on, in most models, I doubt yours is any different.
Very short cycles can be an indicator of low refrigerant, though there are other reasons. Guessing, when adding freon can be catastrophic. The best way is to empty and recover the refrigerant, then add a couple of ounces or whatever you need to get the full 20 ounces and then put the whole load back in. It takess special equipment to do it right, you need a recovery system and a means to weigh the charge. The twelve ounces you added is half the total charge, it is likely you way overfilled it. 600 PSI is dangerous, if something blows it can kill you.
Just adding refrigerant can be done with a manifold gauge set, but takes some practice and skill. Not something a novice will likely succeed at, it is pretty much guesswork and experience. The reason being, the pressure in the system is pretty much constantly changing, there are no perfect/exact pressure numbers. The only real constant is the total weight of the charge is 1.25 pounds or around 20 ounces of freon.
Something to keep in mind, more freon doesn't necessarily mean more cold. Also you have to purge the refrigerant line from your freon container to the compressor. Getting the air in the feeder line into the system drives the pressure up, but doesn't help cooling a bit. IMO unless your experienced, it is best to leave it to the professionals and in my experience the professionals screw it up on a regular basis.
Found this on a google search.
HIGH PRESSURE RELIEF VALVE
DESCRIPTION
A high pressure relief valve is located on the compressor
manifold, which is on the side of the compressor.
This mechanical valve is designed to vent
refrigerant from the system to protect against damage
to the compressor and other system components,
caused by condenser air flow restriction or an overcharge
of refrigerant.
OPERATION
The high pressure relief valve vents the system
when a discharge pressure of 3445 to 4135 kPa (500
to 600 psi) or above is reached. The valve closes
when a minimum discharge pressure of 2756 kPa
(400 psi) is reached.
The high pressure relief valve vents only enough
refrigerant to reduce the system pressure, and then
re-seats itself. The majority of the refrigerant is conserved
in the system. If the valve vents refrigerant, it
does not mean that the valve is faulty.
The high pressure relief valve is a factory-calibrated
unit. The valve cannot be adjusted or
repaired, and must not be removed or otherwise disturbed.
The valve is only serviced as a part of the
compressor assembly.