To be honest, I'm not using these much any longer because I'm conserving the coils in case I won't be able to order from FT at any point, and my husband is wedded to the Nauti Mini (and me, of course!

), so I mostly don't use them myself, to make sure we have enough to last us a while if the time comes we can only buy locally at ~3€ per coil.
BUT without enacting it in the moment, my memory is that I hold the tank upside down, put the drip tip between my index and second finger with the top of the tank lying flat between those two fingers , and hold on to the upside down tank glass with the bottom of my thumb and my index finger, wrapping my other fingers also around the glass, then twist off the end with my other hand while pulling up.
So, in other words, the whole tank is held in a loose (fingers are not curled in) fist in my left hand, which holds it all together, while I unscrew the bottom and then fill and re-attach with my right (prominent) hand.
It's simple, but hard to describe! If this doesn't seem to make a lot of sense I'll try a photo tomorrow. Let me know!