There is no flashing between the wall and the deck which is allowing the water to run behind if that is the area in which the moisture is leaking.
Also unless they put a rubber membrane under the tile water will also seep through the grout. You can seal the grout to some extent to slow down this process, but it is not fool proof and some water will always seep down. The tile is somewhat water resistant, but the grout between is not.
So sense the floor has already been placed, purchase a good quality tile and grout sealer and try that.
Some windows instead of screens could help too...open when nice close when the rains come
Very easy to enclose with Cool-Breeze vinyl panels that can be raised or lowered. Open, you have a screen porch, closed you have a weathertight room!