Judges can issue and likely mostly issue warrants with defined parameters in terms of what can be searched and then usually a pre-delineated list of what can be seized. The latter can be generalized to items like "computer equipment".
One possibility is that LE had some nexus between either DS and FG's vehicles or FG and DS's vehicle which they took to the judge to get warrants.
They appear to have had permission from the judge from the get-go to seize FG's vehicles/vehicles he had access to.
So the judge might've issued a warrant that
(i) allowed LE to immediately seize FG's vehicles and take them in for processing;
(ii) do a thorough "search" of the Oxford house, but nothing (obvious) would or could be seized--unless the police during that initial search hit upon evidence of a crime being committed at that location (.e.g, blood).
Course, as soon as the police Luminol up some blood that seems to indicate a crime occurred (splatter on a wall, or carpet or wherever), the entire process changes and they can either proceed under in plain sight/open and obvious/whatever rules to seize relevant items; or simply call a judge and relay what they found and get an expanded warrant issued immediately. [might even be an app for that at this point j/k (close tho)]
Mobile crime van + dogs were reported at the Oxford house the first week after DS went missing.
which that they waited or had to come back later to seize the mattress (possibly other items as well) suggests they found no easily discernible by trained crime-scene techs evidence of a crime while on location.
Once back at the lab, they managed to find something and used that to get a warrant to seize the mattress? Maybe. Or maybe they got further evidence from another source that caused them to bounce back for the mattress.
It's all a mystery.
