This is a guess, but i suspect it might be a trigger hysteresis thing.
The trigger point of a scope when it's doing an edge trigger is actually more of a trigger range - the signal has to hit two comparators in the right order for the trigger to happen. As a result, the signal can sometimes show up slightly shifted on the screen. Then, scope makers shift the waveform back in software so that it doesn't look funny. You can check if your scope does this by switching from a rising edge trigger to a rising-or-falling edge trigger. The alternating edges make it where the scope can't get away with shifting the waveforms, so it'll appear that the signal crosses the trigger point slightly shifted.
I suspect that for this scope, when channel 1 is not displayed but the scope is triggering on that channel, there's no shift. But, when you turn on channel 1 the hysteresis adjustment kicks in. I'd bet that the timing relationships between the two signals isn't actually changing.
Just a guess, as it's not our scope, but this would be what I would look into. You could try putting the scope into rising-or-falling edge trigger mode and see if you get the shift.