Luke Skywalker has vanished. In his absence, the sinister FIRST ORDER has risen from the ashes of the Empire and will not rest until Skywalker, the last Jedi, has been destroyed. With the support of the REPUBLIC, General Leia Organa leads a brave RESISTANCE. She is desperate to find her brother Luke and gain his help in restoring peace and justice to the galaxy. Leia has sent her most daring pilot on a secret mission to Jakku, where an old ally has discovered a clue to Luke's whereabouts....
If the First Order's plan is to search out and destroy Luke Skywalker, why do they order TIE Fighters to shoot at the BB unit which contains their only means of finding him? Doesn't shooting at the droid containing invaluable data defy all logic and directly contradict the entire plan?
If someone kidnaps the President of the United States and speeds away with him, the secret service wouldn't call for an Apache attack helicopter to blow up the vehicle containing the President, would they?
This is similar to the asteroid chase scene in The Empire Strikes Back when the Star Destroyers were shooting at the Millenium Falcon even though Darth Vader wanted Han Solo alive, but I have theorized that the Star Destroyers were actually ordered to shoot at the engine in order to disable the Falcon (but Han just thought they were out to kill them). The same can NOT be said for the TIE fighters shooting at BB-8 in The Force Awakens, though (for obvious reasons).