that double note thing happens to me all the time.  I posted about a few times.  It has been a while but I believe the solution for me has been the first one mentioned above.  On the receiving midi track set the input to a particular midi device and a specific channel.   Here is a post from another forum where the dude said the same thing and it worked for that dude. "I had this problem also. The answer was that my controller was sending MIDI on two ports (i.e. USB MIDI In A and USB MIDI In B). When I selected "All MIDI Inputs" for the input source for the track, it was receiving two sets of notes. You could tell your track to only accept the input from a specific port rather than "all MIDI inputs" or tell your controller to only send the MIDI data on one port. For my controller I had the choice of "USB MIDI In A" or "USB MIDI In B".
Sincerely,
J.L.
You could also go to Devices -> Device Setup, select the MIDI Port Setup. Here you can tell Cubase which MIDI Port inputs to include in "All MIDI Inputs"."

The Roland A-300PRO is capable of a "dual" mode, or layering, which is very easy to select from the buttons. I'm sure that means it transmits on two different channels "simultaneously". I share brundlefly's skepticism about it because of the relatively large gap between the duplicated notes, but it's worth checking your event list to see if that's what happened.