The DC automatically boost, best option is to just monitor the DC and be prepared to take over. You only need to apply a small amount of throttle to override the DC. Majority of the time the DC will work fine on the Cutter, if it acts weird then override it.
The DC only boosts over 3KM away from the station, haven't had the problem at all since I firstly didn't boost after exiting supercruise and secondly got within 3KM prior to engaging the DC. Saying that, yes the DC should be able to handle the ship from further out and be able to handle the boost etc.