i think you will find that most Milles with a fast onboard vibrator need to be used when cold starting, sounds like most of your bikes have had carbs in the past.
The Mille can be a fickle starter, the late 03 models onwards dont have a fast idle and you just leave the throttle alone and hit the starter, the ones with a fast idle seem to need it set at somewhere between half and full to start from cold.
Should have foregone the £150 of profit on the Benelli:dowhat