I'm curious why they would assume that she would turn up on her own, and delay a search when delaying a search is unusual? Why would they assume that no crime had occurred unless family gave some indication that she might be depressed and bullied?
When there was no evidence that she was alive, they deemed her disappearance a homicide. Dogs followed the route she commonly took to the bus stop. That ruled out nothing. WLAN helped narrow down the timeline that she was using her phone at the house. It seems that stopped at 8AM. At 8:30, her mother texted the brother in law to make sure that she was up for school. This is where it is first noticed that she is missing.
Normally the school phones home when a student is absent, but apparently that did not happen this time. Parents learned about the absence at the end of the school day. That is where the story first started, with the assumption that she left early for school - but that made no sense to her father.
There was very little time between the decision to involve the crime unit, the arrest and presenting a case for probable cause. If they find more evidence after searching the house he, and perhaps his wife, will be detained.
She was staying with her oldest sister, a married 27 year old nurse?