I think you are misunderstanding the "fruit of the poison tree". Any evidence gained from an unconstitutional search is inadmissible. That doesn't however, prevent the authorities from trying to gain that information through an alternate path, thus parallel construction. Intelligence can't be used to get a warrant or used in court without allowing the defense to challenge it.
However it can be treated like any other tip, and as long as the authorities use legal and constitutional means to investigate that tip and to gain any evidence they use to get a warrant, they use evidence the gain as a result of following up on that tip.
Furthermore, evidence is only excluded if constitutional rights were violated, or the legislation that makes gathering it illegal includes an exclusionary rule.
For example the Pen Register Act doen't include an exclusionary rule. Police can use an illegal pen register to gather metadata about a phone call and it is still admissible. The police could be prosecuted for doing so, but the evidence is still admissible. It's the result of the Supreme Court ruling Smith v Maryland which is at the root of much of the recent controversy lately.