Rum didn't force his way into Amanda's room—that would've likely led to it ending up messy. If Asaka was standing outside Amanda's room, if Rum had just began by attacking Asaka, then he'd have to deal with hiding the body—and if Amanda didn't expect him, and noticed Asaka was gone or wondered why her bodyguard let this person in, the room might've become messy as Amanda panicked and tried to defend herself. If Asaka was standing inside the room, then Amanda would've likely noticed the commotion of Rum attacking Asaka, and if their fight spilled into the room from the doorway, Amanda's room could've ended up messy, also because Amanda might've reacted in panic to Rum.
More likely, Rum was let in by Amanda and Asaka, neither of whom thought the former's life was in danger—if Rum was someone Amanda expected, why attack immediately and risk his intent being exposed immediately when he could just slip in casually and poison Amanda under Asaka's nose. In other words, Amanda was killed first, and then Asaka was attacked.
If Asaka wasn't APTX'd, then Rum must've been distracted—likely by Kōji (Asaka Vs Rum might've been underway in the hallway by the time Kōji came into view, or he came into view of the room just in time to see the fight spill out into the hallway). I presume that and Tsutomu's interference bought time for Asaka to regain consciousness—Asaka probably regained consciousness to find Kōji dead. Presuming they'd be arrested, they fled the scene.
Alternatively, Asaka could've been talking with Kōji, thus giving Rum the chance to go and kill Amanda unimpeded. Which then would've led to a fight between Rum and Asaka & Kōji. After knocking Asaka out, Rum immediately hurried to silence Kōji, since if he killed Kōji quick, he could prevent him from escaping, and then come back to silence the unconscious Asaka—silencing Asaka before Kōji ran the risk of letting Kōji escape. After that, Tsutomu intervention, Rum flees, and then Asaka flees.