Kurapika's chains wouldn't work on Illumi or Kalluto
What does it formally mean to be part of the Phantom Troupe?
- having the spider tattoo and an assigned number
- being acknowledged by Chrollo as a member (vague)
But if we follow this way of defining membership, Kurapika has no reliable way to verify any of these criteria. For his condition to work, there would need to be some kind of omniscient mechanism checking who qualifies as a Troupe member — something that simply doesn’t exist in HxH.
So if Nen conditions really depend on personal beliefs and perception, then from Kurapika’s perspective, the Spiders would be the people he personally considers responsible for, or at least deeply involved in, the Kurta massacre.
His goal to eliminate the Phantom Troupe originates from his hatred towards them and sense of revenge, by associating the Spiders with those who killed the Kurtas. He doesn't hate them because they commit evil and criminal actions, in general (he's not a punisher).
So his definition of Spiders is based on this fact.
Back in Yorkshin, he saw the tattoo on Uvogin's back and he had no reason to think he wasn’t involved, so the condition works.
So all the members, part of the original formation are in his eyes responsable and therefore fit with his definition of Spiders. Even Suzuku, since Kurapika has no reason to believe otherwise.
But with Illumi and especially Kalluto, he would be certain they had nothing to do with the massacre, so it wouldn’t make sense for him to treat them as Spiders under his own definition.
One could argue that his definition of Spiders might evolve over time, eventually expanding to include anyone who is deeply involved with the brigate in general. But again, he has no way to verify that. And since Nen conditions are bound to the moment they’re imposed, this expanded definition wouldn’t apply anyway.
EDIT: by chains I refer to Chain Jail, thanks to the person who corrected me in the comments. I deleted the part about Pakunoda because it didn't make sense - I apologize for the mistake.