Looking at it from the point of view that OP did believe an intruder was in his house, I can understand how events unfolded.
When under severe stress or in a panic situation people do not always behave in a rational manner. Some people may freeze, some flee and some fight. In his mind he'd left Reeva moments before in bed. Within moments of him being up he heard sounds, he panicked and in his mind Reeva was still where she was moments earlier, in bed. Does everybody analyse their every word and deed when in a potentially life threatening situation? I don't think so.
I have been trying to think of a motive that would make OP kill his girlfriend deliberately. The most obvious would be, as you say, he caught Reeva texting or phoning another man. We don't know yet who's phone was found in the bathroom. Was Reeva hiding in the toilet texting/phoning, or did OP believe wrongly that this was happening? Jealousy is a powerful emotion.
I hope the prosecution brings this up on Monday. If they don't, then it would appear that this was not the case at all.
Also, in the past when OP had family or friends staying overnight and he heard someone moving about outside his own bedroom, I think he would have stopped to think that it could be his guest, and would have been more careful with his gun. But if he believed the only other person in the house was in the same room as him in bed, then he would react differently because the situation is different.