So, my question is: when a mage who's projected into astral manifests back, is he affected by non-targeted spells like Trid Phantasm or Entertainment?

Dunno, but he'll be able to see the spells aura. He may see the illusion, but still know there's an illusion there.

No, he is not. Manifesting is not making the Mage actually present (Materialized) on the Physical. He is still occupying Astral Space, and he is NOT Dual Natured at that point. Your Physical Spells will not translate over to the Astral Plane, so therefore he is not affected by them.