If you buy an extractor fan and put it in the back of a tent it is a complete waste of money. This was good advise many years ago when spray tans were applied by airbrush and the flow of solution was much more controlled, ie into the tent. The new hvlp guns all spray at 360 degrees so unless you stand in the tent you will spray around and above the tent. You will also get solution bounce back off of your client as the solution hits the client and very fine droplets bounce back into the room. (just blow your nose after a session).
The Cube Inflatable Tent is plastic and solution sticks to the inside of the tent and is just wiped down after use, this will reduce overspray into the room, also the Ravair Vortex Spray Tanning Extractor is on wheels and stands in front of the tent to catch any overspray, full details on the Ambermist website. In any event any extractor you buy should be in front of the tent, any extractor with enough power to pull overspray solution from the room past the client and down into the unit would be too noisy and too powerful. All it would do is suck solution from inside the tent and off of your client.