Pre-slope needs to be in place BEFORE the tiles. Flood test (leak & drainage check) happens before the tiles are placed. Your not properly fixing bird bath's after the horse has left the barn.

If it is not draining properly on the surface it is not draingf properly at the pan. Water sitting becomes stagnant.

Water sitting in the pan will become stagnant which will lead to mold.

A photo of the puddle would help.

If your shower is not draining properly then mold etc could become an issue. The issue is where is the unevenness. If it goes right down to the shower pan liner then that water will never drain and it's a major fix. If it's just at the surface right under the tile then it might be an easier fix. But as your contractor already tried and failed to do a spot repair it sounds as if there's no waterproofing on the shower pan directly under the tile. There are lots of contractors who have been building showers in the same way for many years and just haven't adopted the new standards, methods of construction and modern waterproofing products. I think an honest conversation with your contractor is needed to understand what they did and how it can be fixed.

Water pan liner is not water proofing? the puddle of water will disappear in about 1 hour. i assume it seep below. there is pan liner below.

The pan liner is a waterproof layer, but modern shower construction uses a waterproof layer right under the tile ie on top of whatever the tile is being stuck to. This might be a waterproof sheet like Kerdi or a painted on coating like Hydroban.

OK your puddle could be in a far worse position. You could just help it on it's way after you've showered, I actually wipe the walls and floor of my shower after every use, or get you contractor to have another go at a fix.

The puddle might be slowly draining or the water seeping into the mortar bed below (assuming there's no waterproof membrane on top). In that case if the pan liner is correctly sloped the water should drain through weep holes at the base of the drain.

thanks for the information. if the water is seeping into the mortar, and the pan liner is sloped correctly it is fine. however, if the pan liner is not sloped correctly and water is snagnant on the pan liner, it is an issue, as the water will cause mold issue. is my understanding correct? attached is a picture where there is liner. The contractor was fixing a leak in the remodeled bathroom. (yup he did not test his work)

That's basically correct. It looks like there's not much thickness of mortar at the drain if that's the liner in the photo and that might be part of the problem. There doesn't appear to be any water proofing on top of the mortar bed which is the modern "best practice", but it is the way it's been done for a long time. The way you have things should be ok as long as the pan liner has a pre-slope under it.

There should usually be an inch or so of mortar thickness at the drain to allow for some fine tuning of the height of the drain so it's just below the finished tile. You can either screw the drain up or down a bit or remove a bit of the mortar.

The way to know if the pan liner is sloped is to ask your contractor if they installed a pre-slope under the pan liner.