You are correct - immigration laws are different from criminal laws! As such, a deferred disposition is a conviction for immigration purposes contrary to what your counsel told you. Carry a certified court disposition with you. A letter from an immigration attorney, explaining the petty offense exception and its applicability here, would be helpful as well.
Disclaimer: This answer is for informational purposes and does not take the place of a consultation with an experienced immigration attorney. This answer does not create an attorney-client relationship.