I don't know if this is right, but I let my ring finger rest on the string when I grip the tama. This allows me much more control while flipping the ken.
From an earlier discussion, I think that
starting with the finger on the string (I think of this as a 'trigger', really does change the way the ken flips) would be considered a 'foul' in BKA/JKA terms, though I can't be certain. I think that manipulating the string under the tama after start would be allowed, but better check with BKA/Void/any of the examiners here on the board. Personally I abandoned this technique; after becoming more familiar with 1-Turns and Hanging 1-Turns, it stopped being any real help.
Just to give my two groats' worth, 1-Turn Lighthouse - 'pop up' from your knees and release just before the highest point, and follow the ken through the air moving the tama. Don't know about anyone else but my 1-Turns were terribly inconsistent (had repeatedly landed it but would sometimes go for days with no joy) until I stopped thinking of them having an Aeroplane landing.
1-Turn Aeroplane - for some reason I find this trick easier than 1-Turn Lighthouse. My only tips are focus (as in, really focus, eye-ball the meeting point of ken and tama) and be ready to catch lower than you think, which I suppose is another way of saying 'knees'. Oh, and don't hammer it, unless you want to catch the 1-Turn with your forehead/chin/nose. As much as spectators may enjoy it, tends to give the player less-than-satisfactory results.