I'm not a luthier and I don't know anything about the bass you bought. That said here are a couple points to consider.
If it is at all a decent instrument it will be well worth the cost of a proper setup including board planing, post setting, nut slotting and bridge shaping to get it playing and sounding it's possible best.
Make sure the bridge is installed properly, it should not be too difficult to keep it from coming out but it is not uncommon for the nose of the bridge to creep toward the fingerboard while bringing strings up to pitch.
Try this:
Take a ruler (I have a flexible ruler for just this purpose) and place it across the top straight between the upper notches in the f-holes, with the bottom edge of the ruler against the widest point of the notches.
Set the top of your bridge feet against the bottom edge of the ruler. Now the lower notches (the ones facing toward the bridge) should be about center of the bridge feet. Make certain that the flat side of the bridge is toward the tailpiece and the side that rolls off a bit is toward the fingerboard.
Use a ruler, a small square, or other 90 degree reference to make sure that the bottom (flat) side of the bridge is perpendicular to the top of the bass.
Slowly bring your strings up to tension, "bumping" the nose of the bridge back toward the tailpiece with the edge of your hand if it has moved. This may take a number of tighten then bump the bridge operations. I have never used nylon strings so I do not know for sure.
Another way to bring your bridge back perpendicular to the top is to (with the bass laying on its back - which I assumed it already was) lean over the bass from the bottom and grab the outer edges of the bridge with your fingers and give a tug toward the bottom.
The last point just made me think of a question - your soundpost is still up in position, is it not? If it is not that could be a real problem and needs to be corrected.
Anyway, make sure the bridge feet are shaped perfectly to the curvature of the top and the bridge stays perpendicular to the top. It is not uncommon for the bridge to "nose up" with tuning.
If the feet tend to slip easily put a little rosin dust between them and the top and that should be fixes.
Hope all this makes sense and helps. If not, I'm sure someone more knowledgeable and better at communications than I will be along soon to get you taken care of.