Bro, I don't think there's any way for CNG to cause transmission problems, such problems are caused by careless shift abuse, AFAIK.
Continuesly Variable Transmission aka Vario has got drive belts instead of conventional torque converter, so the risk has even been reduced. Besides, it offers you virtually unlimited gear ratios & 6 virtual speeds, instead of conventional 4 speed auto tranny.
The problem of Vario on CNG is: powerloss. CiTY is already a 1.2L - 78hp ; underpower car, & then you put an auto tranny, A/C & CNG on it... and the result: the car would literally DIE.