Engine Mounts issue can be caused by replacing Alternator?

I think the problem was probably there before and you are just noticing it. Lots of times, the problems we experience with vehicles happens over time. Motor mounts are one such thing. They do not wear out overnight or just give up the ghost all of a sudden (in the vast majority of the cases). Most of the time, as these things wear out, we don't notice it happening. Then, when something major happens (in your case the alternator), we suddenly become hyper sensitive to how the vehicle is running or how it feels to us.

Bottom line is, you'll need more than likely need to get your motor mount(s) replaced as the mechanic suggested (if you didn't have it done already). Motor mounts will continue to wear and if not replaced, will cause more wear to the good motor mounts due to them having to pick up the bad one's slack.

While both Paulster2's and Steve Matthews's have good answers, there is another thing to consider. The 3.5 V-6 equipped Camrys that year (not sure about the 4 cly) have what Toyota calls Active Control Engine Mounts. They use vacuum and electricity to control the mounts. Also on the 3.5 engine it's quite an extensive repair to get to the alternator off, and if during the repair a vacuum line or electrical connector was knocked off or not reconnected it might cause you symptoms.

I am not saying for sure it's the technicians fault it's just worth finding out. As Paulster2 said it may have been there but now you are paying more attention.