Can 12/2/2 cable be used with two circuits on the same leg with the neutrals tied together?
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.