I finally got around to watching this and here is my theory on what exactly happened to the doll. After Retsu gets her dress Killua asks her to give Gon and him the location that she believes to be where the Pairo doll is that contains Kurapika's eyes. After a small argument Killua asks Gon for a moment alone so they walk outside to the alley. Before the even leave the store Retsu uses the Soul
Doll ability. According to the HxH wikia a brief description states:
The ability to make a doll copy of a person that the target is strongly thinking about. Conditions in performing Soul Doll are :
Omokage's doll must be adjacent to the target while that person is thinking of someone. When the doll is adjacent to the target, it will turn into the person that the target is thinking about. The real person of whom the doll is based cannot feel or notice this (without actually being there). ref(Omokage Abilities)
During the brief exchange with Gon, Killua has the ever present flashback of Illumi telling him that he will betray his freinds. After Retz comes out and addresses them in the alley they leave, the scene zooms back into the alley and we see a purplish aura that grows into a humanoid shadow.
So my theory is since Retsu can manipulate her doll without strings she sent it after Gon and Killua in the alley and once the Soul Doll ability was activated it caught on to Killua's thinking of Illumi and once they left the alley it transformed into the Illumi doll that we see later on in the movie.