The short answer is that standard tubs, such as alcove and corner tubs, should always be installed first, followed by the wall panel, subfloor, and vinyl. The tiles in the bath and shower area need to be installed and finished first. Follow that with the floor tile. Tile the entire floor in case someone decides to install a pedestal sink.
Yes, unless there is some REALLY good reason to do otherwise, you should put the tub on first. You, of course, must ensure that you protect the bath well from damage during tile work (several layers of cardboard and tarpaulins, for example). I am surprised that some professionals don't understand this. Tubs are usually installed before tiling.
However, if you want to add a bathtub to an otherwise finished space, or at least to a tiled space, you may want to know if there will be any problems placing the tub on the floor tile. The principle of tile installation is that the tiled wall “hangs” above the tiled floor. The best way to achieve this result is to tile the floor first so that the wall tile appears to be “sitting” on the bathroom floor. Separate sink and wall kits are often used to replace old tub combinations in bathroom remodeling.
Four potential problems can arise when installing a bathtub on a more delicate tile, such as ceramic, porcelain, or stone. If you add a bathtub to an existing bathroom space or other area of your home that already has finished floors, it would be more cost-effective and less time consuming to install it directly above the tile.