Where is the water coming from? Is there a drain our outlet or something allowing water in... or is the water seeping right on in through the cement? Why does the water look so brown, is there debris or dirt of something getting in there?

A permanent sump will need to be installed to handle the ground water. We do this very often.

It's not good for the structure to have that amount of water behind after a fresh shot. They should have continued to run the pump. Also, constant moisture will have an affect on the plaster's ability to bond properly. It's much like painting on dry wood as opposed to damp wood.

We are currently building a pool on the Hudson River in New York and (2) permanent pumps will be installed to handle the ground water when the tide comes in. Right now (2) temporary pumps are in place.

They pick up water about 18" below the bottom of the pool floor.

I would also recommend an automatic hydrostatic relief plug. It has a spring loaded cap in the event ground water pressure exceeds the pool water pressure. Essentially a fail safe in the event the sump pump fails. It allows an for exchange of water to hopefully prevent a pop up.

We will install a drain cover over the top as well.

I don't know jack about pools but I know a little about pop-up, and I was worried when I saw the pic that it was going to happen NOW because there's no water in the pool to hold back the water pressure from the ground. But obviously it's leaking somewhere, so maybe that will alleviate the problem. However...your brand new pool leaks. What's that going to cost in water over the next couple of decades? I'd be asking the contractor that. As I said, I don't know anything about pools but I'm pretty sure they are not supposed to leak muddy water.

The water is most likely coming up through the hydrostatic pipe installed when the pool was shot.

The water is muddy as the soil beneath the pool is coming up with the water table.

Pools can still float despite being completely filled with water. Groundwater can be very powerful.