Mila placed her ear close to the door, she wanted to listen closely to know when Zyran leaves the room. Earlier when she had arrived and met a young man working in the living room, Mila didn't know why he was there until she saw the shaman's phone.
It was very obvious what was going on, Zyran was trying to check the woman's conversation. Either he was trying to find something the woman knew that he didn't want outside or he just wanted to figure out who killed the woman. Two things were sure, either Zyran had killed the woman or not. There wasn't an in-between. And to find his position in everything, Mila needed the information to come to her first before it gets to Zyran. And she didn't want him to know what she had been up to since she returned.
From the look of things the young man was yet to make any progress, Mila didn't want to look too interested or it would get Zyran suspicious.