There's not one bit of inference in the article that the FBI left the sites open one moment more than it took them to bust down the doors.
From the article --
Unbeknown to the paedophiles, the two sites which they were using had been seized last year by agents from the Federal Bureau of Investigation.
.....
In October, detectives in the US arrested the websites' owners and seized the database.
I don't see where it says they closed it down. It does seem to imply that the customers continued to use it after it was siezed.
And, anyway, you seem to think they messed up if they shut it down. There is obviously not enough info in the article to say for sure whether they did or not. I hope they did shut it down immediately. And I hope they don't sell heroin to children to solve underage drug-use problems.