I think the comparison of flying 4th finger with famous flying finger for holding a tea cup very funny. In the tea situation I always thought brain is just avoiding damage from touching the burning cup. when I drink beer my finger does not fly, maybe because it is too heavy...
So I would take care of this. You are thinking wrong when you think you are not worrying. It is going up because you are worried. Learning to release it means learning not to worry. You are affraid, but you shouldn't, the guitar strings are not burning out...
Lovemyguitar made the important point. Don't learn to hold it down against your worries and your fear of playing well. Learn to release your worries and relax, so it doesn't go up in first place.
You can actually learn to release while holding it down. I recommend fixed finger exercises, not to forcefully hold it down, but simply to put some focus to this finger, so you keep using it, you get used to it, and you learn not to fear this finger anymore...
For example, keep 4th finger fixed in a pedal note while other fingers play scales, like the exercises 1-6 and 15-18 in Carcassi Op59, end of part1, page 38 of the pdf in the link below:
http://carkiv.musikverk.se/www/boije/Boije_1129.pdf
You can also practice this kind of exercises without actually playing the pedal note. You may keep finger 4 just slightly touching the string in total relaxation, while other fingers go up and down the fretboard. Look at this independence exercise from Pavel Steidl. Pay attention to his recommendations:
https://www.youtube.com/watch?v=vvdhuP0m9DA#t=2m00s
Practicing slurs with 4th finger may help too.