My understanding is that SWAT deployed to execute a warrant. The traffic stop was news to me, so I assume they ran once they saw/heard SWAT coming. Reports seem to bounce between a stop and a "chase" - either way, SWAT took him. That was around 6:30pm east coast time (4:30p local).
My understanding is the search warrant was executed before SWAT returned. It would be reasonable to assume they will not announce the search until detectives have completed any evidence gathering to avoid media flocking to the location