When opening lanes on punt/kick-off coverages, DB's are trained to push/force the gunners out of bounds and protect the boundary (I.E. keep them outside since the gunners get to the returner first). Punt/Return coverages are usually a 2-on-1 affair with the gunners, who are usually pushed/forced out-of-bounds, getting tag teamed. There is only a penalty when the person who is pushed/forced out touches the ball first.
Any offensive/defensive player can go out of bounds (Without the ball), but once back on the playing field cannot be the first player to touch the ball.
On the play, the Dolphins' gunner was forced out-of-bounds and tried to accelerated ahead of the double team (Which is legal) thus being tripped by the Jets' coached (Who admitted it).