Designing Kitchens and Bathrooms - water leaking through old bathroom tiled floor

Water seems to be leaking from an upstairs bathroom to the downstairs bathroom ceiling. It seems to happen when water winds up on the floor (spill over from the right side of the sink and the left side of the shower). Just running the water in the bathtub and the sink does not cause any dripping.

The house is old and floor also pitches down towards the corner in between the sink and the tub.

I would like to redo the floor and level the corner. Underneath the tile is plywood. After removing the old tile and any backer board, should I throw on some leveling compound in the corner?

For further security, can I place some sort of plastic liner in between somewhere before the final tile goes on?

Just running the water in the bathtub and the sink does not cause any dripping.

Something doesn't sound right here. Do you really get that much water on the floor when you use the sink, or shower? Why so much water on the floor from use of the sink? Are you using a shower curtain or glass door?

Hi, it's not me actually, it's the neighbors upstairs. I don't know why there's so much water coming from the side of the shower and the sink or what they do, it is a bit careless.

My bathroom is directly below and the ceiling is removed currently so I am able to see the upstairs plumbing. I;m going to sheetrock my ceiling soon but I can't until the upstairs is figured out.

The upstairs sink is being replaced as well with a pedestal sink. The floor does seem to be the culprit.