Check to see if the Supernova remains in performance mode rather than
Program mode - if it switches to Program mode, the Supernova has received a
bank change / program change message corresponding to the Program mode. If
it remains in performance mode,  look at the set up for the Supernova II
within Logic - has this been defined as a multitimbral instrument? If not, I
think it needs to be - I think this is the most likely cause of the problem.

If however the cause is due to the prog mode, here is some additional info
which will be useful.
There is a bank change map in the back of the Supernova II manual,

bank O = Favourites,
1= Perf A
2 =B
3=C
4=D
5=Prog A
6=B
7=C
8=D
etc.

A bank message is a CC# 32 message with a value of one of the above. Logic
also has "bank buttons" which may be used to select the appropriate bank.
These are used as follows:

If you have the global midi channel on an independent channel, channel 9 for
example, and you are using the multi ch1-8 template (performance A126),
you have:

part 1 , midi channel 1, Logic track 1
part 2 , midi channel 2, Logic track 2
part 3 , midi channel 3, Logic track 3
part 4 , midi channel 4, Logic track 4
part 5 , midi channel 5, Logic track 5
part 6 , midi channel 6, Logic track 6
part 7 , midi channel 7, Logic track 7
part 8 , midi channel 8, Logic track 8
  global midi channel 9, Logic track 9

to assign program C120 to part 5, send the following message from Logic:

on track 5, either press "bank button #7" or transmit CC32,007 from the
sequencer followed by prog change 120.

Whereas to put the Supernova II into the program mode on program C120:

on track 9, transmit CC32,007 from the sequencer followed by prog change
120.

as you can see the message is the same, but because the midi channel is
different (one for a part and one for the global channel), the message has
different results.