We made great connections on Thursday at BUR from our Alaska Airlines flight to #775 for SBA. The flight was a few minutes late but so was the train. We walked to the platform but spoke with a woman who I saw get off the shuttle. She said that the Lot D shuttles will take you to the Amtrak/Metrolink platorm but you have to tell the driver. We also noticed that there is a call box at the drop off point if you are going the other direction and need the shuttle.
I hope that helps anyone who might be making this connection and is not able or inclined to walk. I can see thow it would be nice to have the shuttle if it was bad weather (NEVER happens in Southern California!) or if you had lots of luggage.