Post a picture of the 2 cdi connectors and wire colours.

IFF (IF AND ONLY IF) you are getting constant spark too (which means that your plugs are giving you spark like while welding) constant 12V supply *cannot* be the problem because as greg correctly stated you have to interrupt power supply to coil primary winding in order to cause discharge at it secondary winding (effect of electromagnetic induction). Constant 12V connection (e.g. unintended grounding of coils while ignition is on) would cause coils to heat up but there would be no spark at all.

Messed up wiring might be the cause but I am not able to imagine pin change which would cause such effects while not damaging the CDI.

One potential cause might be some voltage instability inside the CDI (it is new; aftermarket; refurbished or chinese clone?) which causes the CDI CPU to reset upon attempt to charge the coils. OR very very theoretically CDI type which is originally suited for different type of bike (different pickup wheel / wiring) which makes CPU confused...