I bet it only does it when you start it in D or R. Never when you start in N.
Ya, this is normal. You should wait about 15-30 seconds for it to build oil pressure. If you just crank and go it will do that. You will notice it more when cold. When cold you should let it run maybe 90 seconds or so to warm up. That's my suggestion anyways.
I will try starting in neutral, I bet it solves the problem. Waiting for it to build pressure before driving is not the issue, it literally shuts off in 1-2 seconds, before I have a chance to even think about moving.
On the Rincon there is a sensor somewhere. If you crank it in gear and you do not give it a few second or so it will cut off every time. Its just like you said, like someone flipped the kill switch.