In this scene, the atmosphere is most a consequence of suddenness. Richard's behavior changes completely when informed of the loyalty to the princes. The change suggests instability to the audience, which further heightens the feeling of dark and evil tidings. If the temper can shift that quickly and become so murderous, the person must be unstable and illogical. This is not a person guided by morals or ethics.
Furthermore, the effects of Richard's temper change are evil in nature. If his assertions can so quickly lead to Hastings death, than the whole system must be unstable and corrupt. Hasting himself muses on this before death. Also, the quickness of Hasting's turn of fortune creates an atmosphere that is unsettled and unsettling. The audience feels uncertain as to the safety of any character, and thus, the feeling of evil doings is increased.