Shift-right click.
I'm talking about 1.12, some earlier versions can't do this. I think it was added in 1.10...?
A.
1. Set the machine to fill the right side, per the arrows. Place the fluid cells in the machine, let it fill the right tank.
2. press the "swap" button to swap left and right tanks. (See red outline)
3. Set the machine up to either use or empty the left tank, as needed.
B.
Alternately, build and set a Tank next to the machine. Place the cells in the input of the tank, and either set a fluid ejector to the tank (they can be shift-clicked on a side to be directional) or a fluid puller in the Machine, and pull from the tank.
C.
Or shift-right-click... and don't miss the machine or you'll have a watery mess on your hands 
