For the TCU type, just take a look at the label printed on top of it. Somewhere it should say "GSM"; if there is no GSM anywhere then it is a CDMA.
I think that the M3 code is different from the regular 3 Series code from the point of view of the iDrive/Assist relationship, because so far nobody with a pre-03/08 M3 has been able to retrofit this knob and got it working -at least in this forum.
My theory was that at 04/08 the TCU changed from CDMA to GSM and that was the only major hardware and software mid-production change in the M3 in 2008. But now your are saying that the new controller works fully in your 03/08 M3, my theory is out the window unless your M3 has a GSM TCU (a very late 03/08/almost 04/08 production)...