Your AC has a drain pan designed to hold condensation. It also should have a pipe which allows the drain pan to empty outside away from the home... not under the home.
I am sorry but I don't understand what it is that would need to be seamed? We use 3/4 PVC pipe for drain lines here. Sections are glued and it matters not how many "seams" there are.
I have owned several dozen manufactured homes in Central Florida, where humidity is our number one natural resource

Any and all installation standards call for the condensation to be drained away from the home.
Water leaking through to the underside of a home can bring mold, mildew, wet rot and termites. The results could be harmful to your health and the structural soundness of your home
Any professional installer knows this. It sounds to me like they did the install the cheapest, fastest way possible. That it is just wrong.
Call the contractor and let him know you expect them to fully correct their "error". That must include replacing the insulation that got wet and repairing or replacing the "bottom board". Bottom board is a water resistant usually black plastic like material that the floor insulation rests on.
Be sure everything is dried out prior to replacing the insulation. The bottom board should be cut, the wet insulation removed and discarded, the area sprayed with anti mold spray (available at Lowe's) and then left to dry out for a few days. Don't let them button up the bottom while there is any moisture in the floor or you will have mold problems later.
Don't let them reuse the same insulation even if it is dried out. Once rolled insulation gets wet it becomes compressed, looses insulation value and could still hold mold spores.
If the bottom board is cut cleanly it can be closed up using a tape made for that exact purpose. Dont use duct tape as it is not appropriate for this applicaiton and will not last
If you don't get them to eat the cost NOW you will have to do it sooner or later. The longer you wait the more damage will be inflicted and more it will cost.
If you get any resistance or have any doubts call your local building department and ask to talk to the guy that inspects air conditioner installations. I doubt that he would ever pass a system that dumped water inside the home.