Nope. Criminality and jurisdiction have nothing to do with affiliation.
Koris and Konmel both saw themselves as parts of Klingon society, attempting to bring it back to the old ways. Furthermore, both were members of the Klingon Defense Force.
Menos used to be a Vulcan. Then he left Vulcan society and became completely independent. The card reflects both parts of his story, which is not only why he can be in "Vulcan" mode, but only has "V'Shar" when he's in "Vulcan" mode. That reflects Menos while he's still a V'Shar agent. If you put him in exiled "Non-Aligned" mode, he loses that skill, as he has left both the V'Shar and Vulcan society.
Thomas Riker still considers himself a member of the Federation, as he's a Lt. Commander. He's just all alone on the planet he was left behind on, but he still thinks of himself as a member of Starfleet, and has recently been rescued by the Enterprise on the card you linked to.
Later on, he joins the Maquis, but he's still a member of the Federation and believes in it broadly. Furthermore, he's trying to help other Federation citizens, who have been abandoned by the policies of the Federation government on colony worlds. That he's doing so via illegal means has no bearing on his citizenship or his self-identity or his affiliation, just as James T. Kirk remained a member of the Federation even after he stole the Enterprise to save Spock's katra.
There's nothing notorious about Vash. She considers herself a member of the Federation, even if she's shady and breaks some laws. Criminality has no bearing on affiliation.
Kasidy Yates works for the Bajorans, hence the Bajoran mode. She also is a member of the Maquis, who at that point had declared themselves independent of the Federation. Furthermore, she operates outside of the Federation, so it's not clear to me that she considers herself a part of Federation society. All are reasons for her being non-aligned, which have nothing to do with criminality.
Arik Soong's affiliation is completely inappropriate. He's not a member of Starfleet, nor does he work with them cooperatively. Instead, he tries to subvert them and manipulate them for his own ends.
You cannot be a citizen of Starfleet, as Starfleet is an institution, not a government. You can apply to Starfleet, and they can accept you, and you can be a member of Starfleet, but never a citizen. By the same token, you cannot be a citizen of the United States Military.