Electrical – use a three wire cable to feed a whirlpool tub

This is an unfortunately-all-too-common wiring error, even without a 12/2/2 cable to further confuse things. Most folks (even electricians) think "I'll just nut the neutrals together" since that's what works when everything in a box comes from one branch circuit, which is the case 99.9% of the time -- in the 0.1% case, such as yours, though -- this rule leads to a looped neutral, which violates 300.3(B):

(B) Conductors of the Same Circuit. All conductors of the same circuit and, where used, the grounded conductor and all equipment grounding conductors and bonding conductors shall be contained within the same raceway, auxiliary gutter, cable tray, cablebus assembly, trench, cable, or cord, unless otherwise permitted in accordance with 300.3(B)(1) through (B)(4).

and 310.10(H)(1):

(1) General. Aluminum, copper-clad aluminum, or copper conductors, for each phase, polarity, neutral, or grounded circuit shall be permitted to be connected in parallel (electrically joined at both ends) only in sizes 1/0 AWG and larger where installed in accordance with 310.10(H)(2) through (H)(6).

This is easy to fix, though -- make sure that the neutrals in your 12/2/2 cable (white and white/red striped, or "candy cane wire" ;), are not nutted together anywhere.

Not being there, it is hard to say for sure. But a fair guess is the the J-box wiring takes care of the heat. This wiring includes the wall stat/timer. (Hopefully this is the 12-gauge wire.) The other two cables take care of light and exhaust fan. So: j-box cable to red and white in fan. The other two, take your pick, color to color.