He planned to pretend he received a phone call from Nevill. He couldn't kill Nevill in his sleep and yet still claim he received such a call. He shot June first allowing his father to start to get up before targeting him expecting him to fall dead by the nightstand and likely planned to then put the phone back. But he ran out of bullets before he could kill Nevill and things progressed to the kitchen so he didn't bother replacing the phone.
That is one hell of a risky plan! Not quite buying it.
To make things fit, one moment Jeremy has to have been cool and calculating, the next, a blathering idiot leaving behind the most obvious and incriminating evidence.