Then....explain why the "Citizen" was excluded from seeking the presidency after a certain time had gone by [Article II; Section I; Paragraph 5]
There are three categories; Naturalized Citizen, Citizen and Natural Born Citizen. Your own Constitution verifies this by grandfathering "Citizens" from seeking the presidency. Why do you think they did this?
The reason is in the debates during the Constitutional Convention. In early August, several delegates put forward the idea that Senators needed to be native born. James Wilson (who was born in Scotland) gave a speech in which he said that that it was unfair that he would not be allowed to be in the government he was helping to create.
Shortly after they added both the NBC clause and the grandfather clause.
Several other delegates were not born in the colonies, including Alexander Hamilton.