How can I arrange for issues to be assigned?

IF the target project is not under the control of JIRA ServiceDesk then the following applies, otherwise, no assignee can be defined as only Agents can assign tickets.

User > Enable automatic issue assignee : ON

This will get JEMH to assign an issue to the first component owner, if available, failing that the project lead, if applicable. This is useful when your JIRA doesn't allow unassigned issues.

Project > Project Mapping > assignee

Can be defined such that email for a given project can be assigned to a nominated user other than the Project Lead,

Project > Project Mapping > Rule > assignee

Can further be defined to use a specific assignee when the Rule applies, eg 'bill' is the assignee for remote senders .*@faraway.com

Email > Assignee Auto Select > Use first valid user as assignee? : ON

Use the first assignable JIRA user in the email as the assignee, starts with TO, then CC.

Email > Addressee Processing > Addressee Handling : *firstCCIsAssignee*

The first CC entry is tested for assignable, and if valid, used.