Yes, the FBI were coming not matter what. The subpoena from the FBI to Pence and his lawyers, as noted even in your AP article, used the J6 investigation as its pretext. If the FBI conducted the search because of the found documents, as many tell the story, the pretext on the subpoena would have listed the found documents. It doesn't. The subpoena was sought using the J6 investigation as a pretext. Pence's lawyers delayed the FBI by insisting on negotiating a schedule, and they used that time to have a team pre-search before the J6 subpoena search took place.
The J6 pretext used in the subpoena, the negotiation of schedule conducted by Pence's legal council, the search conducted by Pence's lawyers before the FBI got there, and the subsequent search conducted by the FBI is all in the AP article. I don't understand what you are taking issue with.