Im unsure of the details. But I’d assume that they already knew what was on his computer from previous inquiries. If they’d just had access to that computer today, I doubt it would have been enough time to catalogue the brief of evidence and present it to court. Just my opinion.
In saying that, I doubt they’d get a search warrant to go through someone’s computer from an anonymous tip off. August was four months ago, so they clearly had the evidence required already. Maybe they thought he was trying to abscond for good.