Jira Software (Cloud) integration not updating Jira Assignee on Asana

I have created a project in Asana which include the Jira Cloud App. The integration is configured as follows:
Step 1: synchronise at task level;
Step 2: When a jira issue is added → create a new task in asana
Step 3: When a jira issue is updated → update the asana task

In the list of fields to sync i have summary and description which synchronise to asana task name and description.
Status goes to a custom Jira Status on asana.
I have a custom Effort field in Jira which goes to a custom Jira Effort in Asana.
So far so good, all this fields synchronise properly. However, i can’t get to have Jira Assignee field to synchronise in asana. No matter if a choose the Asana standard assignee field or a custom field Jira Assignee. The user i’m testing is a member of the team, the project is public to the team but in any case he is also among the project’s members (even if as a guest)
Any idea?