Welcome to the forums, Jae!
As far as I know different keyboards can behave differently with respect to how their octave/transpose functions affect their MIDI output:
- The octave/transpose functions may or may not change which MIDI Note values are transmitted by the keyboard.
- The octave/transpose functions may or may not cause the keyboard to transmit MIDI tuning messages.
I believe the first possibility is typically the case-- shifting octaves or transposing the keys will change which MIDI Note values are generated by the keys.
However, you should monitor the MIDI data coming from your WK-3700 to verify whether the Note values change as you shift octaves and transpose the keys, as well as whether any MIDI tuning messages are transmitted.
(One of the notes on page E-43 of the WK-3200/WK-3700 User's Guide says that "Changing the ... coarse tune, ... causes the corresponding MIDI message to be output," so apparently the "Coarse Tune" function generates a MIDI "Coarse Tune" message; but it doesn't say whether the "Octave Shift" function generates an equivalent MIDI "Coarse Tune" message.)
If the WK-3700 lets you shift the octaves and transpose the keys at the same time, then in theory you could transpose the keys by as much as from -48 semitones (-4 octaves) to +48 semitones (+4 octaves). That could shift some of the keys outside of the valid MIDI Note range, in which case the nearest valid Note would presumably be used.
Now, if the problem you're having is that the controls on the keyboard don't seem to let you shift octaves "live" in your iPad's virtual instruments, you should try setting up some Registrations that have the channels shifted or transposed as desired, and see if you can shift octaves by recalling the appropriate Registrations.
According to the chart on page E-40, the UPPER1 part uses Channel 1, the UPPER2 part uses Channel 2, the LOWER1 part uses Channel 3, and the LOWER2 part uses Channel 4. So you should be able to set up those four channels with different octave shifts and transpose settings, save them as a Registration; then set them up with different settings and save them as another Registration; etc. That should let you do things like split the keyboard between two different virtual instruments on your iPad, and transpose or octave-shift one VI without affecting the other, or change both VIs at the same time, by recalling the appropriate Registrations.