The short answer is that he must apprehend a threat. In order to justify use of deadly force, the threat being apprehended must be one of suffering serious personal injury or death, or, if a woman, rape.
looking at Prosser, Wade and Schwartz's "Torts - Cases and Materials" 9th edition, on page 104 under the heading of "Self-Defense," point No 6 says (without giving any case cite):
Retreat. One basic disagreement in approach to the privilege of self-defense focuses on whether the defendant must retreat if he can do so without increasing his danger, rather than stand his ground and use force. It is settle that he may stand his ground and use any force short of that likely to cause serious injury. The common law was that, rather than kill his assailant or seriously wound him, defendant must "retreat to the wall." A minority of the American courts still apply this rule, and it is adopted by the Restatement (Second) of Torts Sec. 65. The majority, chiefly in the south and west, have insisted upon a higher important of the dignity and honor of the individual and have held that the defendant may stand his ground and use deadly force, and even kill his assailant. [Remark about retreating from a gun bearing assailant skipped]
No relevant for this case, because this case involves the use of deadly force. But, for use of force that is not deadly, see Restatement 2d Torts Sec. 63. Self-Defense By Force Not Threatening ..., although it is legalese. See "m. Actor's duty to retreat."
The actor, if he reasonably believes that he is threatened with the intentional imposition of bodily harm, or even of an offensive contact, may stand his ground and repel the attack by the use of reasonable force, which does not threaten serious harm or death, even though he might with absolute certainty of safety avoid the threatened bodily harm or offensive contact by retreating.
Thank you for the explanation! :)