If nothing else, put a pan or something under the joint...capture the drips..plus, leave the cabinet door open...get the interior drying out.
The reason silicone and other methods of goo or tape won't provide a permanent fix is that the water is 'pushing out'. That will just go right past the stop gap stuff.
The place where you tighten...don't reef on it. A gentle touch is needed. It might be that something has been pushed against that black piping and now the alignment is out..allowing water to seep out. If it is the large black knobby thing...you need a fairly wide mouth tool...often called a Plumbers Helper. Home Depot, Ace or Lowes will have those in a package of three..about 20 bux for them. Tell a sales rep what it is you want to do...don't be buying a pipe wrench. You don't need that.
If you can't get a wrench till tomorrow...use a dish rag or small towel in your hands..that black piping in your hands slips really easily.
Gary Haupt