It makes sense that the only time party affiliation could be stated or inferred from election records is at the primary. In the general, all the parties are on the ballot, and a person is not expected to tell the election official which party they will be voting for in the general.
On his primary voting record, the article you cited says this:
But his primary voting record is thin: just a New York City mayoral primary in September 2013 and a primary election for a U.S. Senate special election in September 2010.There is no indication that he has voted in a presidential primary of any kind since 1989, a time-frame during which he has said he was a Democrat.
What is your source for the claim that "there is no record that Trump ever voted in a Republican primary election in New York City"?
The title of the Daily Mail article states:
“...New York records indicate he has NEVER voted in a Republican presidential primary...”
I assumed everyone understood we were talking about the “Presidential” primaries.