I think that the fact that Parris internalizes Proctor's presence in court represents much of his reaction. Parris is open about the animosity between both men. In Act III, sc. 3, Proctor starts the process of criticizing Abigail. Rather, than dispute the nature of the accusations or even remaining silent to them, Parris personalizes the antagonism between both:
Excellency, since I come to Salem this man is blackening my name.
This statement represents Parris' reaction to Proctor in court. Parris is more concerned with his own status and eliminating all potential threats to it. In this, he sees Proctor as a threat to his position and his stature in Salem. Parris' reaction to Proctor is one whereby the pursuit of truth is secondary to making sure that his own position and reputation are beyond reproach. When he senses that Proctor's presence in the court could threaten that, all attempts are made to ensure that Proctor is not successful in his pursuit of truth and justice. This is why Parris exclaims joy at the end of the scene when Proctor confesses.