The anemone ended up way more bubbly than that pic.  I also had to move it out of the tank again into a NO lit tank, while I kept the lights off in the 120g to get rid of some cyano.  Kept the bubbles in that tank, kept the bubbles when I put it back.
Then I changed the bulbs.  (from Hamilton (ushio) one year old, to new Ushios). (Lights were slowly re-introduced)
Low and behold, no more bubbletips... 
 
So, I'm wondering, is this their way to increase the surface area of their tips for some kind of lighting reason?