Electrical (3way switch and wire but single pole)
You are calling it 3-way switch wiring.  Actually, it is simply 3-wire wiring and has nothing to do with 3-way switches.  This type of wire is used in all cases 3 conductors +ground are needed. 

3-way switches just happen to be one of them.  

In this case, the cable is carrying 3 wires besides ground: 


Neutral, white  (needed by supply, fan and onward circuits)
Always-hot (needed by supply, switch and onward circuits) 
Switched-hot (needed by switch and fan) 


The preferred color code, where available, is black for always-hot and red for switched-hot. 

I prefer to re-mark wires with tape to color code them.  By luck, all the cables already have the preferred colors. If it were me, I would remark the hot wire on the fan with red tape, then fit a red and black pigtail on the two switch terminals.  Then it becomes a simple matter of matching up color to color! 

Pigtailing the red on the switch may seem a little silly, but it's easy to grasp.  

One more thing.  Since 2011, anytime you wire a switch where the power comes into the lamp, you must use that 3-wire cable.  Red and black for the switch. White is reserved for neutral for future smart switches.