It looks like the problem is that because the bottom surface is tile, the vinyl sweep doesn't close where the grout is because its lower than the tile. So water leaks out all the grout lines.
How are pivot doors (without a botto rail) like this normally installed on tile surfaces?
Should I run a line of caulk along the floor so the vinyl sweep hits against that? That seems like it may look a little strange.
Perhaps just caulk in the grout lines? Again, I think it might look strange.