I wouldn't be surprised if he murdered her, left her in the apartment, cleaned himself up, then went to the gym, called a bunch of times to cover his track, work himself up in a rehearsed state of panic to sound convincing over the phone to the 911 operator.
A psychopath has a shrunken amygdala, which means as a result they feel no fear, remote, guilt, or shame, they have no emotional empathy as well and an overdeveloped pre-frontal cortex which results in serious control over all their impulses and the ability to hide their nasty side from anyone they want and unleashing the nasty side when they feel it's safe to do so with unmasking. Hence why they can easily compartmentalize a kill, move on fast from the act, and go straight home like nothing happened. But they are extremely skilled at faking emotions to sound distressed, afraid, in panic, etc... to make anyone believe them.
Hence why, I wouldn't be surprised if the fiance is faking everything this entire time since the moment he left the apartment at 4:45 pm.