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 am utterly confused. Any help please?

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