The main problem with short generator runs is the condensation in the exhaust and in the oil.
If you don't heat up the oil enough, moisture will not evaporate, and it will cause internal damage over a long period of time. Usually 10 minutes works fine to heat up the motor enough if it's aluminum.
Exhaust however, takes longer, especially if there isn't a heavy load on the motor. Hold your hand to the exhaust. If it doesn't feel really hot or if it leaves your hand damp, then it should be run a bit longer. Moisture condensed in the muffler will rot it out quick, as in a year or two.