I think I see what might be going on here -- at least part of the time. Simply put, on some of the voices, when you select the main voice, it automatically turns on dual voice -- and I believe that octave piano is one of these situations. This is because not all of the "main voices" are strictly and solely contained in the "main voice" part of the keyboard. For some voices, Yamaha determined that to get the fuller sound that a particular voice may call for, it needs to be combined with another voice, so certain main voices do this automatically. In other words, for some of the "voices", the sound is not designed to be just a single voice, but a combination of two voices, which are automatically put in the main and dual voice slots.
So, assuming octave piano is one of these voices, Yamaha determined that it couldn't get a good enough octave piano using just one voice, so when you select it, the keyboard turns on a piano voice as the main voice, then automatically turns on another voice (in this case, likely another piano voice an octave higher or lower than the main voice) with the dual voice. So, when you select the octave piano voice, and then turn off the dual voice as you described above, you are changing the sound that Yamaha intended for the octave piano voice, and are likely losing the extra octave part and just remaining with a basic piano sound.
Now, as I said before, in any case selecting a main voice automatically causes the keyboard to set up a dual voice that Yamaha feels goes well with the main voice, but the keyboard does not normally automatically turn on the dual voice, unless you select one of these "double sounds" where the main voice is designed to work with a dual voice for the overall tone of the "main voice" selected. I believe that when you then go from one of these "double sounds" to a main voice that is just a normal sound not designed to be combined with a specific dual voice, then it turns off the dual voice mode, which is probably why you're seeing dual voice turn on and off they way you are as you go through the voices.
So, what happens when you use one of these "double sounds", that automatically turn on dual voice, as the actual dual voice? You just get whatever would be in the main voice slot as the dual voice -- and whatever the keyboard would've automatically added as a dual voice, just does not get added. As an example, if selecting the octave piano sound as the main voice gives you "piano sound A" as the main voice and "piano sound B" as the dual voice, and you instead select the octave piano sound as the dual voice, then you only get "piano sound A" as the dual voice, and "piano sound B" does not get added at all.
So yes, if you use the octave piano sound as the dual voice, it will sound quite different than when selected for the main voice, because you are not getting the extra octave piano part of the sound. And when you use a sound like this as the main voice, then if you do change the dual voice sound manually, your sound would likely be different than you expected, because as we know, you cannot have three voices layered, so using the octave piano "piano sound A" and "piano sound B" example from above, if you select the octave piano sound as the main voice, but then change the dual voice to a brass sound, you'll just have "piano sound A" and "brass", with "piano sound B" now removed, overwritten by the brass sound.
This is something that my E433 does, as well. So, when Yamaha advertises something like "780 sounds", or whatever the number is for the E425, it isn't REALLY that many, because some of those sounds are just automatic combinations of two of the other sounds available on the keyboard -- in my experience, the main voice in one of these "double sounds" is a duplicate of one of the other sounds on the keyboard -- though you may want to double check that -- they could've updated that in the newer keyboard, but I doubt it. On my E433, I believe the literature states 731 voices, including these "double sound" voices. When I looked at how many "double sound" voices that includes, I figured that the keyboard really has about 600 or so truly unique, single-sound voices.
The data list, showing all of the sound selections, should indicate which ones are "double sounds" that automatically turn on the dual voice.
EDIT: Note that when I originally typed and submitted this, I included information implying that the dual voice sound information stays the same as you change sounds except for when you use one of the "double sounds" described above, but that is incorrect. Whenever a new main voice is selected, the keyboard automatically selects a new dual voice set-up, overwriting what was previously set as the dual voice. But the keyboard will not automatically turn on the dual voice, unless it is one of the "double voices."