I looked up AutoZone part numbers and they don't have the same number. The RAV4 has a 2.0L 4-cyl while the '96 Camry uses a 2.2L 4-cyl...different engines altogether with different spark requirements. I'd take the RAV coil back and demand the coil you paid for.
You've got an OBD-I engine block in an OBD-II car. Which ECM did you use? The '96 or '93? These engines have different codes and running parameters, and there are more parameters being analyzed on the '96 that may not be capable on that '93 block. But you don't mention any trouble codes, so I presume you got that part hooked up correctly.
One thing I learned from changing timing belts is to set the crank and cam at 0° TDC and then mark the crank's and cam's timing gears with the current belt position and then transfer those marks to the new belt. Otherwise, you can have the cam and crank aligned at 0° TDC, put the new belt on, but upon turnover the crank will start turning before the cam due to slack in the belt...they go out of sync and runs like crap that way.
So, recheck the timing marks and adjust, clean up the cap & rotor contacts, get the right coil...might as well check those plugs for fouling and clean/regap. Hope this helps!