Your LU should hold 15 PSI without leaking. If you used a hand pump, it is not likely that you could pressurize that much. Oil coming out of the prop rear usually means that the a seal is shot. As mentioned, oil should be pumped in from the bottom hole and with the top plug removed. As soon as oil starts to run out of the top hole, you have added enough oil. Replace the top plug first before unscrewing the fill hose from the bottom. That helps slow down the flow from the bottom when the fill hose is removed but regardless some oil will leak
One thing to do next time is to roughly estimate the amount of oil that drains out by using a container that allows you to estimate the volume. My LU holds about 1.1 quarts of oil and if I don't drain at least a quart, I would suspect that oil has been lost during normal operation and further investigation is in order.
In your case, you have to remove the prop ( you should do that every season anyway to check for things like line wrapper around the shaft) and inspect the shaft seal for evidence of leaks.
The only true test of the LU is a pressure/vacuum test. There are two seals on the shaft: One keeps oil from leaking out and one keeps water from leaking in. For the later, a vacuum test is required.
Of course if you saw water in the drained oil, you don't need a vacuum test, you need seals. Keep in mind that there are other seals than can leak. The drive shaft seal and the shifter seal. Leaks are hard to see with the LU attached but will show up with a pressure test.