First off, the wall needs to be properly set on stone for drainage. And it may have the need for drain tile. As you know, water is going to be making its way 'along the path of least resistance', ie., your wall. Sooooo, you need to collect it, AND, get rid of it. (I'm assuming that the landscaping in front of the wall is relatively level. If it's a wall that's set, say, midway on a hill, you may not need to undertake the aforementioned drainage measures.
Now, in ALL cases, before backfilling is done, you need to do 2 things. Get some filter fabric. NOT landscape fabric. You local Gravel Yard or Stone Quarry carries it. If not, ask them where to get it. But UNTIl you get it, keep the contractor away. Once you lay in the fabric, you neede to backfill a bit with gravel. By putting the gravel between the dirt and the wall, you PREVENT the water from getting anywheres NEAR the wall. The purpose of the fabric is to keep the dirt from 'polluting' your gravel BUT allow water to pass through. You need to 'grade' the dirt before you lay in the fabric such that the water can 'safely' make its way under and out from behind the wall. If you DON'T do this, water pressure will 'push' your wall out where there's the least amount of resistance.
There's more to say but it's not that complicated. I've included a link for you to read to familiarize yourself with retaining walls. Educate yourself so you and the contractor will understand each other. The Allen Block WEB Site is a very good one for DIYers. There's DIY info and drawings and technical info for ALL levels of expertise. If you have more ?'s, post up.
My best to ya and hope this helps.
PS: After this afternoon, I won't be back until Monday. But, in the meantime, keep your contractor at bay until you get the job 'ready' for him! Oh, forget about who is right or wrong for now. Learn the physics of the problem and you'll answer that question yourself in due time.