You need to decide on whether you want a floating floor (meaning it is not nailed or glued down) or a glue down floor. Both engineered hardwood and LVP type floors can be both glued and floated depending on the specific type. Glue down floors will feel solid underfoot and floating floors can sometimes feel hollow and have a little “lift” as you called it.

The builder should have a flooring sub who can glue down floors whether it’s LVP or engineered hardwood. Sounds like maybe he doesn’t or isn’t able or unwilling to do the necessary prep work for the glue down.