Wrong. He did not die for everyone! As we are clearly told in the verses below - that all and only those the Son died for, they must become reconciled to the Father and saved.
The unsaved by not being reconciled weren't those whom He died for. IOW, by the Son's death, that everyone covered by it must become reconciled to the God, so those unsaved weren't covered.
i.e., death of the son = reconciled.
[Rom 5:9-10 KJV]
9 Much more then, being now justified by his blood, we shall be saved from wrath through him.
10 For if, when we were enemies, we were reconciled to God by the death of his Son, much more, being reconciled, we shall be saved by his life. ...