Eyebrow tattoo removal PicoSure after ND YAG, ink turned brighter red (Photo)

Bright red eyebrows should be always be discussed prior to treatment, as this is a common and expected occurrence.
The reddening of your brows comes from oxidation of the ink commonly used for brows. It is not the same red as a red ink, per se, unless the tattooer compounded an ink color containing some form of red, which would be unfortunate. Thankfully, it appears from your photo that these are very commonly encountered iron oxides.
My recommendation is to find a practitioner experienced with eyebrows, staying away from those who would fiddle and play with settings with an actual patient in their chair. Medical lasers are not toys, and people handling them need to know the chemistry and physics of what they’re doing. Oxidation and color shifts are a part of informed consent, and every one of my patients understands this in detail before we even start. 
The good news for you: It’s all cool! With continued treatment from a professional, your red, oxidized brows will vanish. Until then, your eyebrow pencil is your best friend. 
Good luck to you!

Laser removal of tattooed makeup can be particularly challenging because the inks used are different than the ink for body or decorative tattoos . Often times the patient (and the person applying the tattoo makeup) don't have a good idea of the exact ingredients in the ink. Many of the inks used in tattooed makeup contain iron, which when lasered can oxidize and turn the tattoo into a rusty brown, red, or black color. This is why I typically don't perform laser tattoo removal of tattooed makeup at my practice. I find that the appearance of the tattoo during the tattoo removal process is so unappealing to most patients that they would rather let it fade over time naturally. With many repeated laser treatments this oxidized pigment can fade over time, but it will likely take quite a few treatments.