Also, at that moment, they believed she and the girls were missing and possibly in danger so that might be enough for probable cause regardless of consent. But I agree, I do think he gave consent. Jmo.
You do need a warrant when you're investigating a crime and even if the suspect gives permission you would want a warrant typically.
But he was not a suspect at the time. And he gave consent. It was a welfare check and a husband pretending to be scared about the welfare of his missing family.
Now if the phone was locked and he didn't know the password it depends on the phone company if they would allow the husband to create a new password. It is his property.
Otherwise they probably would require a warrant.
No matter. They have it all now.