I don't really understand what you are saying. Does your contractor propose to construct the "footer" from the ground up? If so, this would be highly unusual, and likely a very bad idea, but maybe I don't understand the plan. In general, footers for a house need to start below frost level, but they are also buried because the soil strength increases with depth for a variety of complex reasons. However, without an exact description of what is proposed, I really can't make a judgement.
One question though, do you have plans for the house, do you have a permit, and are you subject to building codes?
The footers will be covered when the dirt is filled inside the stem wall. They will be built by 2x4s and 1/2" plywood, and filled. 2 courses of block on top of the footer for the stem wall and back filled and compacted after that.