Most people tend to use thin cyano these days, holding the wood in place and running the thin cyano behind to stick it instantly, some use pva behind to bond it and just cyano to tack it, both ways work
Most PVA is not waterproof , some are more water resistant than others such as aliphatic and aliphatic resin, both are pva just with an aded resin,
Some pva is a crosslinking pva , this means that after the water is lost from the glue it then cures like the cascamite type using a similar catylist that is inbuilt into the adhesive, stable while wet and fully waterproof when dry (after about a week of losing the water it becomes resistant to even hot water), all our PVA and the Aliphatic resin is now of the crosslinking type formulation, most available are not crosslinking (none in general use we have found to have been crosslinking types)