Claire had remembered to include something about the timing in the email last minute without telling Alex he wasn't as rushed for time anymore. He had told her once that the only ones who stayed at headquarters full time were some guards and the Numbers. Searching the place in the middle of the night wouldn't catch anyone important.
The FBI had probably raided the warehouse by now since it was about noon. Conducting a somewhat-willing kidnapping must have confused them since they went there to save kids and all the kids were gone. Claire wanted to personally ensure that they were taken care of instead of immediately foisting them off onto strangers.
Besides, she doubted the FBI would be understanding of Logan and Lucas, who had already killed people a few times under the guidance of older agents. Ray's social worker sister-in-law was a safer bet.