I created a 'remote portlet' (on JIRA instance A) pointing to an 'Assigned to me' portlet in another JIRA instance B.

The portlet appeared fine, but all its links points to the JIRA instance A not B.

The HTML source suggests that the links in the remote portlet are relative, and so these are interpreted as relative links to instance A and not B.
Because you enter the remote instances URL (seperately to the portlets key when configuring the portlet) that the relative links are pointing to the remote instance as well.