The engine in your Primera should be the QR25DE. According to the Wiki page, it should be equipped with a steel timing chain, not a belt. Your mechanic is spot on. Timing chains are usually good for the life of the engine (rare occasions otherwise).
A timing belt/chain connects the camshaft and crankshaft together, making them work as one. The camshaft rotates at half the speed of the crankshaft, but timing is crucial between the two (therefore why it's called a timing belt/chain). They are used on nearly all overhead cam designed engines. With the proper covers in place on the engine, you won't see the belt/chain at all. You are correct in thinking the serpentine belt is not the same as the timing belt/chain, but are wise in keeping up maintenance on it. They do wear out!
There's no easy way to tell without dismantling part of the engine. You may be able to take the front top cover off of the engine to see (this should be an aluminum cover which will be on the front side of the engine - to the right side of the car as you're sitting in the driver's seat) . Everything I've been reading show the P12 with the 2.5l engine to have the QR25DE, which is chain driven. I don't think you'll have anything to worry about.