When you load the MIDI file into Cubase and play it, is it using HALion Sonic SE to play the sounds?
OR
Are you rerouting the tracks to your PSR via MIDI?
I’m not sure about LE, but in Cubase Pro, by default imported MIDI files will attach to a bunch of independent Sonic SE instances. So, if you want to send the output of the tracks to another plugin (or even to a single instance of SE, but in rack mode multi-timberal mode), or to some MIDI port for an offboard workstation, you’d need to reassign the tracks to do so.
Not sure about LE (worth a try), but in Pro, You can change the MIDI output of several tracks at once by first holding ctrl and selecting all the tracks you wish to change (so they highlight), then hover the mouse over the output entry in the track inspector, then to select an output for all of highlighted tracks.

Also be advised that Sonic SE isn’t configured as a General MIDI plugin by default. So, it’s not necessarily going to call up the right sounds if/when it gets MIDI program change events.
Also, with Sonic SE, if you’ll be working with General MIDI files, you’ll want to hand pick the drum kit you wish to use, and put it on Channel 10. Note, you get several General MIDI mapped drum kits to ‘choose from’. Subsequently, if you are working with a General MIDI II file that uses a drum kit on channel 11, again, you should manually place the kit of our choice on channel 11 as well.

Note, if you would like to force a different patch to a given program change (over-ride the basic GM soundset), you can do so by lowering the ‘rank’ (star rating) of the sound in question in the media browser, then assigning any other sound you like the same program number, and giving it a ‘higher rank/star rating’.
If for some reason the MIDI file you wish to play tries to call up a drum kit using a Program Change on channel 10, you can either remove, filter, or mute the program change event (using your key-editor) so it won’t keep changing the program/kit you have loaded in SE. If you intend to make a true General MIDI compliant File, you should NOT have a program change event on channel 10. GM1 protocol assumes the kit is just there on channel 10 and ready to go. GM2 has other methods for ‘changing kits’ (GM2 files will usually work in GM1 players…as a GM1 player just ‘ignores’ things it doesn’t understand, and uses its standard kit).
There is more to discuss in regards to how General MIDI files drive FX units, and how that correlates to HALion SE in particular. SE will accept CC events for reverb and chorus in so far as adjusting the ‘send’ levels, but you’ll need to set the reverb and chorus (types, and fine settings) you want it to use by hand in the SE UI itself.
As for options on importing/exporting MIDI files…there are quite a few of them. More on that later if you ask. For now I must get off the computer and go take care of some things.