The problem is the wall is plasterboad and the fixings supplied are for a solid wall.
Fixing bathroom sink to wall.
For a slip joint leak first tighten the slip nut.
Many people may try to band aid the problem by recaulking the edges of the sink backing to the wall.
If so replace them with slightly thicker ones that you have to tap in with a hammer.
Check the shims after refastening the cabinet to the wall.
Amazon tool shop here.
Fill the sink bowls then as they drain check all joints from the sink to the wall with a dry tissue see photo above.
Insert wurly fixings into the holes these are known as metal plasterboard fixings at the builders merchants.
They may be loose because the screws lifted the cabinet slightly.
How to fix it.
Now that you have made the repair to the water damaged bathroom wall all that remains is to finish off.
The wall is plasterboard and the sink is fairly heavy it also is the freestanding type ie the pedestal is not to the floor.
Offer the sink up to the line and get someone to mark the screw holes through the sink which can be found at the bottom.
I have a sink basin for a bathroom to fit.
Drill the holes with a 5mm wood bit.
If the wall was tiled replace the tiles and grout.
Run and drain the dishwasher and check the waste hose connection.
Wall mounted sinks have a great modern look and make a small bathroom especially a guest bathroom seem less cluttered and more spacious fortunately mounting a wall sink is a doable project for most diyers.
Finally cut and install new base trim before applying silicone to the inside edge where the drywall and tub meet to create a watertight seal.