but...this is specfically talking about the Electoral College...it DOES meet on the same day for all states.
Let's look at the text again: "The Congress may determine the Time of choosing the Electors, and the Day on which they shall give their Votes; which Day shall be the same throughout the United States."
IMHO, it looks like "the Time of choosing the Electors" (what we know as election day) could be covered by the last clause. And not just "the Day on which they [the electors] shall give their votes."
I honestly don't know.