My 2004 Mazda 3 jerks when switching between drive and reverse?

When i start my car, the AT light on the dash pops up and remains there. Shifting from P to R (reverse) stalls for 2 seconds and enters gear with a jerk. The same thing happens when i switch between reverse and drive. I drive a 2004 Mazda 3.

The mechanics say I have a Ford engine installed, which is quite powerful, which is he reason for the jerk. I recently took it in to be serviced and i was told the transmission is fine. With doubt, i took it to another auto-shop and they said the brain box installed isn't a Mazda brain box, and that was what caused the jerks. At these two scenerios, i'm utterly confused. Any help please?

So the brain box is the wrong one then and so does not work correctly with the car - why doubt that piece of information.

Get rid of it. That car will only give you headaches with repair costs now and in the future. The mechanics are unable to figure it out exactly because it isn't common. You may end up paying for repairs you don't need because they can't explain what the problems are since it was put together by someone else.