Yes indeed, this starting condition it very normal, more instinct really, from the times when you were taught to not keep the starter engaged once the engine had started. The real cause is and has been stated before and recently OIL pressure is simply not reaching the Oil Pressure switch from a not used state the oil journals drain back from the block into the oil pan and when you are starting the set it just takes a few seconds longer that what your normal sense of engine starting is more used to.
When in fact the starter has already dropped out of being engaged as determined by K-14 i think it is. K-14 is a VOLTAGE provider, it is driven from the MAG pick-up or sending unit as it might be called, but none the less, the MPU counts the flywheel teeth as it spins and make a very slight voltage out of the chopped square wave pattern of the MPU generating as a voltage, this MPU signal is converted into a small voltage and then applied across one of the small chipset devices mounted onto the circuit board as can be seen when you pull or look into the K-14 relay device. thus when the flywheel spins faster from a dead stop to rated speed the small chopped signal is converted into voltage and the ckt board thro and to the small 8 pin chip set, so the starter has dropped out, by your continuing to hold the S-1 switch in "START" position you are also sending a signal the the injection pump to keep the fuel solenoid open and distributing fuel to the engine respective injectors .. Then in this same sequence of starting events oil has finally reached the OP switch and has forced the switch closed thereby completing the ckt and your set will keep running just fine and you can release the S-1 back to its normal run position and all is well.
As a side bit of information when i converted my sets to full auto start just when a signal is called for i had deep reservations the set would respond to being able to Auto Start and stay running. But it does and has every time. I use these 10kw [mep-803a] sets as prime back-up power sources for a local FM low power radio station and a MEP-802a 5kw set at the Transmitter site as well..The 5 and 10 kw sets use identical control schemes and control cabinets, just running a 4 cyl engine V. a 2 cyl engine ..I forget the frequency of the MPU signal at 1800 rpm but it is near 2800Hz .. As an FYI I have about 15 extra K-14 relay units and am pleased to offer them at $60.00 shipped.
Good luck man and these are great little sets to have and use .. best mac/mc