It does take a while for construction water to move out of the building. Concrete, drywall, paint, wood, etc. From what you have described, the basement is humid. Circulating air (wrong time of the year) or a dehumidifier will reduce this. You probably should do this in any case.
The reason for the wet is that although your have insulation, it is not air tight at this point. So what is happening is you are keeping the insulated walls at a lower temperature (from the insulation) but then letting warm humid air behind the insulation. Result - condensation.
The fix is to put in a vapor barrier. However it is not good practice to just cover an exterior poured concrete wall without a vapor barrier on the wall (concrete block, never never). You may also be getting more water diffusion through the concrete than you want. The barrier should extend under the headers and footers to channel water out of the wall structure if stray condensation does occur.
Put the vapor barrier on the concrete, then reinstall the insulation. Closed cell spray foam would be the best solution (it is insulation and vapor barrier) but it is expensive. With a vapor barrier on the exterior wall you should not put a vapor barrier under the finished wall surface. It will trap any moisture that leaks in. If the condensation is ONLY interior humidity you could seal the finished wall. But you would really have to seal it perfectly. I would seal the outside wall myself. If you can remove or get behind the framing that would be best. Seal joints in the vapor barrier by folding over and sealing with a pliable caulk rated for the material inside the folded over joint. Taping is used but I don't trust it.
Generally be sure you do not generate any water pressure on the foundation. Don't dump rain spouts at the foundation. Everything else you need to do, it is too late if the foundation is already back filled.