I cannot stress this enough: If there is any way you can physically remove the rock and, perhaps, chip the anemone off, ensuring you get the anemone and a small piece of the rock he was on, I very strongly recommend you do that instead of any other method.
Like you, I had a single Aiptasia come in my tank with a coral. I even saw it and I figured as long as it was there by itself I wouldn't worry about it. Eventually, it turned into two.
I got the Joe's Juice and followed the instructions precisely.
Long story short, Joe's Juice just seemed to make them mad. They'd disappear for a while, shrivel up, and then come back to life and create two more in the process. Within about 8 months they had overrun my tank to the point where I ended up tearing the tank down.
In fact, I even put the live rock into a tub of saltwater, outside in Monterey, California where it was 55 in the day and in the 40's at night, for about two weeks, covered in the dark, and the anemones were still everywhere. Utlimately I had to put them in a tub of freshwater to kill them off (and my live rock).
For every story I've read about using Joe's Juice or boiling water or Pep Shrimp, I've read another about how none of these techniques work.
If you have the option, do the hard but sure thing and take the rock out and physically remove the anemone and the surrounding substrate.
You have to decide if the risk of trying the other methods is worth it.
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