What is the correct action if someone joins the prayer beside me, following me as an imam, without me having intended to lead, and is it incumbent upon him to inform me of his following, or should I ask him when I notice him praying beside me?

The validity of the follower's prayer is not affected by his following someone who did not intend to lead the prayer. The prayer of the one who was followed is valid. It would have been appropriate for someone who senses that another person is following him to intend to lead the prayer to attain the virtue of congregational prayer. It is not permissible to ask him during the prayer. It is permissible to inform him before he begins his prayer in any way, even with an audible voice.