I got water there from time to time. A couple of things to try:
Double check the connections on the water filter cartridge (or bypass if not installed) and at the taps, it may not be coming from the drain. These can loosen up over time and drip.
If the black rubber gasket on the sink bottom is dry, try to revive it a bit. Armor All can help with this. You can also try smearing a bit of Petroleum Jelly on the sealing surface to make a better seal.
If you use a bucket or similar to catch the grey water runoff (we used a plastic cat litter container with a screw lid for easy transport to the bathrooms for dumping), make sure that there is an air gap at the end of the hose. If the drain hose is inserted below the waste water level, the sink will drain slowly, and there will be back pressure that might force water around the gasket.
2011 Jayco X19H (purchased 2015)
2008 Jayco 1007 PUP (purchased new, traded for the X19)
2012 Chev Traverse LT with TP