It's good to keep track of which way a pot is wired. All the schematic symbols for pots that I have created have that information as part of the symbol.
For pots that are not 'B' (linear) taper, such as audio volume controls, it's not only good, it's necessary, because the resistance change for a given angle rotation is much different at one end compared to the other. The consequence would be that the volume is very high over most of the rotation and then suddenly drops as the pot is rotated mostly CW, with reasonable volume levels being very hard to set.
It's intuitive (to me anyway) that clockwise rotation of the shaft should increase the brightness in this case, so you would want to connect the pot so that happens. (You should also add a series resistor so that the maximum current is limited and does not damage the LED and/or pot).
In fact, it's functional either way, and with a linear pot, not much different.
And, as others have suggested, it's typical to connect the "open" end of the pot to the wiper, which slightly reduces the wiper noise and has other beneficial effects.
As far as current flow, the simulator diagrams show conventional current, which flows from + to -, so in the direction of the arrows. Electrons flow the opposite direction but you don't need to worry about that in most situations.