So I would say that if you spray water at every other front door with a hose, water would get in at at least 90 percent of the front doors. That is far from reality.
Well, water does not flow upwards yet. You wrote yourself. The tiler installed a slope. Therefore, it should not accumulate there because it can and will flow off due to the slope.
One would still need to know if your front door is on the weather side. If not, I wouldn't worry about it at all. Driving rain from the east or north is as rare as a tornado.
I don't know exactly. The tiles right at the door have a slight slope... see photo. But the next tile seems almost underwater. That's also where the water pools (2nd photo). I'm not starting with the hose again... that was already enough effort and mess. But you mean if it rather comes at the level of the entrance door. I would have intuitively rated that worse. Because then it doesn't just run straight down, but goes directly into the gap.