The electors being "appointed" simply means that they are chosen for that office. They may be chosen by election, they may be chosen directly by a state legislature, some other mechanism might be used. The Constitution leaves that entirely to the states.
3 U.S. Code § 1 says:
The electors of President and Vice President shall be appointed, in each State, on the Tuesday next after the first Monday in November, in every fourth year succeeding every election of a President and Vice President.
When it says "every election of a President and Vice President" it means the vote of the electors. Thus it says that the electors are formally appointed four years after the previous set has done so.
3 USC § 7 goes on to say:
The electors of President and Vice President of each State shall meet and give their votes on the first Monday after the second Wednesday in December next following their appointment at such place in each State as the legislature of such State shall direct.
So they are appointed in November, and then vote in December.
3 USC Chapter 1 does not refer to "election day" in any sense meaning a popular election
Note that these code sections dates from 1948.
The Federalist #68 says, in relevant part:
It was desirable that the sense of the people should operate in the choice of the person to whom so important a trust was to be confided. This end will be answered by committing the right of making it, not to any preestablished body, but to men chosen by the people for the special purpose, and at the particular conjuncture.
A small number of persons, selected by their fellow-citizens from the general mass, will be most likely to possess the information and discernment requisite to such complicated investigations.
Another and no less important desideratum was, that the Executive should be independent for his continuance in office on all but the people themselves. He might otherwise be tempted to sacrifice his duty to his complaisance for those whose favor was necessary to the duration of his official consequence. This advantage will also be secured, by making his re-election to depend on a special body of representatives, deputed by the society for the single purpose of making the important choice.
All these advantages will happily combine in the plan devised by the convention; which is, that the people of each State shall choose a number of persons as electors, equal to the number of senators and representatives of such State in the national government, who shall assemble within the State, and vote for some fit person as President. Their votes, thus given, are to be transmitted to the seat of the national government, and the person who may happen to have a majority of the whole number of votes will be the President. But as a majority of the votes might not always happen to centre in one man, and as it might be unsafe to permit less than a majority to be conclusive, it is provided that, in such a contingency, the House of Representatives shall select out of the candidates who shall have the five highest number of votes, the man who in their opinion may be best qualified for the office.
The above makes it clear that popular election was expected to be used to choose the electors, although it was not used by all states at first, and was not invariable until after 1860.