If you desire, any spell you cast whose range is touch or greater can originate from the projected image instead of from you. The projected image can’t cast any spells on itself except for illusion spells. The spells affect other targets normally, despite originating from the projected image.
Polymorph is a Transmutation spell, not an illusion spell. If you cast Polymorph, your illusory double can't target itself. Your shape would change as normal if you targeted yourself. Your illusory duplicate would mimic your actions but be unaffected by the Polymorph spell. Since it doesn't say the illusion is adjustable, it would still look, sound and smell like you, not like a creature's form you've later assumed.
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So you cast it and it always looks like it did when you did so, even if your looks change. Why wouldnt it change to mimuc the caster? Say the caster waves his hand, shouldnt the image do so? Pulls out a wand? See, i see it as it will continue to change as you do, as it is a reflextion of you. I dont think it is the most popular view though.