In the preperation for Hatchet City, I'm fairly sure Vincent advises you to have a custom move prepared for when Blind Blue gets to use its mind control power on you. Blind Blue's move is *not* In Brain Puppet Strings. Though you can use that for inspiration if you want, it's going to be fundmentally different because it's not Blind Blue that rolls dice, it's the PC victim.
I can't remember how the one I wrote went, but a short and simple version might be something like:
When Blind Blue gets some time alone with a PC, it'll implant a suggestion. Have the PC roll +weird. On a 10+, they resist Blind Blue's mind control and gain some insight into the web of psychic manipulation that the mutant is spreading. (Barf forth some tasty details as appropriate.) On a 7-9, Blind Blue's suggestion sinks deep into them, they can mark experience if they carry it out, and they're acting under fire if they don't. On a miss, they come to some time later having already carried out Blind Blue's will.
Anyway, that's just a quick idea, I'm sure you'll come up with a better one! Don't worry if it's confusing at first, but do read the book and the Hatchet City play notes, most of the answers to your questions will be in there somewhere.