The white tank neck could have a crack in it that opens up when the valve is screwed into it.
The tank liner could have a crack in it and the water is lightly spraying up just at the top of the fiberglass that wraps around the neck.
Either way the tank is leaking and depending on how old it is, and if the softener is not a big box type, it could be under warranty; most tanks have a 5 year warranty. So call whoever you bought the softener from if it is within the last 5 years. CORRECTION, that should be 10 years.
Otherwise you need to buy the same size and probably brand of tank since it is a twin tank softener. There is a label on the tank somewhere that will give you the manufacturer's name and the model number is the size; like 1054 is a 10" x 54" meaning you have a 1.5 cuft tank. I sell tanks.