CBP definitely has authority here. They were conducting a search for a fugitive based on reasonable suspicion (information from ICE). The search could just as easily have been conducted by the local airport police agency. (Jurisdictions have laws that probable cause exists and a police agency may arrest an individual when a police agency in another jurisdiction provides information that a valid warrant exists.)
This search would be defended on several levels - the first of which would be that it was a consensual stop.
The search would also be allowed both under Terry (reasonable suspicion) and under the exceptions allowed for suspicionless searches for special populations.
Further, Courts would rule the search allowable because the government's interest in arresting the fugitive outweighed the level of intrusiveness (merely producing ID). The Court would especially point out that the intrusion (producing identification that was needed to get on the plane in the first place) was so minimal as to be negligible.
TSA only matches names on ID to names on BPs to allow an individual to enter the screening checkpoint; TSA does not check to ensure the person who passed through the checkpoint actually got on the flight indicated on the BP presented to the TDC.