Where did you ever hear it takes several years to cure? It's a basement, not the Hoover Dam? I looked over all sorts of info on curing times, and the longest I see is up to one year, and that is going to be some thick concrete. At the most typical pours, you have the 28 days for maximum strength, and then 3-6 months for all moisture to go out.
http://www.laticrete.com/portals/0/tds/tds183.pdf
Is it a black paint, or is it an asphalt sealer?
You do know what they say don't you? Spend it now, or spend more later.
From what I see, you have a foundation that is not sealed in the corner. How are your downspouts ran? Is it just a short elbow, or do you have the downs going out about 5' or so from the house? If not, then do so. If you have to mow up close to the house, then buy the downs that flip up, and add an extension to them to get the water away.
Also check your grade of ground. Is it higher at the house, then gradually slopes away? If not, then you better order a few loads of topsoil. You may also want to peel back the plastic that you have on the walls now and use something like Dry-Lok or UGL to coat the wall(s) inside.
One thing I see also in the picture is that it looks like there is moisture around the black drain pipe. Is there moisture there? And is so, just per chance, can it be coming from up around the pipe.
Like I said, don't let the contractor jerk you around. Get him there, have him look at it, and worst case, he brings in a backhoe and has to dig down at both walls. The walls should be sealed with an asphalt sealer that is normally sprayed on, and not a black paint.
Good luck, and be sure to document EVERYTHING!!!!