I can't speak for the Borgias specifically, but a noble family wouldn't have an "assassin" under their employ in the way we think of it. Certainly any aristocratic household would have a fair number of soldiers and retainers that they could call upon to perform violence on command. The murders of both John the Fearless and of Louis, Duke of Orleans were carried out not by a sneaky guy doing parkour all over the castle, but by the simple expedient of knifing them. The assassins in both cases were not specially trained murderers dressed in black. They were the standard sort of retainers and members of the household that any aristocrat would have maintained in his service. In wartime, they would have served as a formal part of their lord's retinue. As these incidents show, they were quite capable of violently serving their lord's interests outside of a formal battlefield as well.