Here's what I think is happening.
At the beginning, you had a dilute solution of salt.
As more time passed, some of the salt dissolved and some of the water evaporated, and you had a saturated solution.
Still later, as more water evaporated, you got a supersaturated solution.
Eventually, as water continued to evaporate, crystals deposited, especially where the solution met the walls of the container.
These crystals served as "wicks" up which the solution could climb by capillary action.
Evaporation continued all through this process, and eventually you had crystals extending all the way to the lip of the container.
I'll bet they looked something like this.