Okay, if the connection is AX7 MIDI OUT -> Triton MIDI IN, then what you're doing on the Triton can't possibly make it back to the AX7. (You could, of course, get a second MIDI cable and connect the Triton MIDI OUT -> AX7 MIDI IN, so that playing a note on either keyboard could use either or both keyboards to make the sound, but that's a whole other story and is probably more than you want to do now anyway).
I'm not familiar with the AX7, and Roland's website doesn't have the manual, so I can't give you exact help, but I can at least point you in the right direction. What I'm describing may not be exactly how the AX7 does things, but is probably pretty close, if not right on.
Most keyboards have two different types of sounds: a single sound (a patch, in Roland terminology, or a program in Korg terminology), and a larger group of related sounds (a program in Roland terminology or a combination in Korg terminology). To keep it simple, I'm just going to call any one of those sounds.
Switching from one sound to another within a bank will send a MIDI program change (PC) message, and switching from a sound in one bank to a sound in another bank will send both a bank change and program change message.
When you switch between patches or programs on the AX7, you're probably sending a program change and maybe a bank change message to the Triton, so what I'd have expected is that the Triton would be the one changing sounds quickly; this is what I suggested might be happening in my last post. Are you sure that you don't have your MIDI connections mixed up and that you're not going from the Triton's MIDI OUT to the AX7's MIDI IN? I'd bet that you are, because otherwise, there's *no way* for *anything* you do with the Triton to affect the AX7. Take a look at that first; it's most likely your problem.
If you do have the connection from Triton to AX7, what's happening is that the Triton is sending a program change message and the AX7 is responding to it and changing the sound. For whatever reason, that's putting the AX7 into upper mode only: probably, the new sound selected on the Triton sends a MIDI PC message that corresponds to a sound on the AX7 that is in upper mode only. For example, say that you're selecting program or combination #10 in a bank on the Triton. You're sending a MIDI PC 10 message to the AX7, which responds by switching the sound on the AX7 to whatever the 10th sound is in the current bank. In your case, that happens to be one playing the upper part of the keyboard only.
If all this is as I've described it, you've got a few options. The simplest is to not connect the two keyboards, which means that each must play its own sounds only. It's simple but limiting. There are two other options if you do want to have both keyboards make sounds on the Triton (or both keyboards make sounds on the AX7).
1) From the sending keyboard (whichever one has the MIDI cable in MIDI OUT), turn off the ability to send MIDI PC messages, either globally (MIDI PC will never be sent on MIDI OUT) or on a sound-by-sound basis (i.e. switching to sound #10 won't send a PC message, switching to sound #11 would). You'd also want to set up sound #11 so that the MIDI PC event that was sent would be whatever goes well with the sound on the sending keyboard (which isn't necessarily sound #11 on the receiving keyboard). Example: the Triton is sending to the AX7. You play program #11 on the Triton, which is strings, but want to switch the AX7 to program #1, which is a grand piano, so you end up layering strings and piano together.
2) From the receiving keyboard (the one with the MIDI cable connected to MIDI IN), turn off the ability to receive MIDI PC messages globally. You probably can't turn this off on a sound-by-sound basis, and it would be weird to want to.
Make sense?