I made a tart with a filling of blended berries and yolks. The filling wasn't runny, but it soaked into the pie during cooling and the bottom got soggy. When I did more or less the same recipe with a lemon filling, it didn't occur (and the dough was softer, even though the butter was nice and soft and didn't melt). Why did it happen? I baked the cake without the filling. Then I poured the filling and put it into the fridge. Should I have covered the base with egg before baking, would that form some sort of protective layer?  
You got a soggy bottom because there was too much water in the filling. Water in the filling has to be absorbed by something in the filling, otherwise your crust will absorb it instead. There are a few ways you can improve the result:  Reduce the water in the fruit, commonly this is done by cooking the fruit down until it is thicker Add starch to absorb the water, if you are cooking the mix then cornstarch works well for this, if you want to keep it cool use arrowroot powder Use gelatin to stabilize it, note until it gels some water will get into the crust Coat the crust to prevent water from soaking in, a thin layer of white chocolate or milk chocolate does a good job, a layer of corn syrup also can work, although those will add flavor  