This isn't really honestly true, unless the Democrats succeeded in changing the history books to clean up their image, as they seem to continuously attempt.

Sure Lincoln wasn't on the ballot in the 10 southern states, but you were responsible for having your own ballot printed, or having your political party or supporters in other states do so. Elections were more of a write-in and frequently people didn't know of all the candidates from other states. The country relied heavily on representative electorate voting. You would vote for your local electorates, whom have pledged their support of a candidate you liked.