I'd trust screws more than post inserts in a light wood like paulownia. Bridge posts aren't an issue as almost all the force is downwards, with just a bit of fore-and-aft pressure at times when tuning or bending strings. But the stop tailpiece post inserts have to counter the string pull towards the neck and also upwards to the bridge. I think paulownia is the wood that the Pit Bull hollow and semi-hollows have bridge blocks made out of, and it's never particularly impressed me as being very strong, so have always used the longest inserts I can find for the stop tailpiece.
Don't forget that with a Fender style bridge, you can always use longer fixing screws of the same diameter for a bit more grip and load spreading. The standard ones are typically about half the body depth, so you can normally add an extra cm or so to the screw length if you want to (plus it adds slightly more mass to the body). And with string-through bridge, the strings are also helping to hold the bridge in place.