EDIT: Another interpretation of the statement suggests they take responsibility for the event by proxy of deterring said aircraft which was then targeted by friendly air defences.

EDIT II: Prev. statements by Houthis suggest they had formulated new tactics to tail fighter craft with drones/missiles a while back so probably more likely that had something to do with it.

Ansarollah have historically followed up with evidence of such claims against UAE/Saudi aircraft of the same generation. They definitely have the capability, but no hard evidence yet.