That strikes me as odd -- I've never seen separate lines for Republicans and Democrats. Where I voted there was just one line (and it was a long one, at 7 a.m., no less) and there was no way to tell who was voting in which primary. Only the poll workers would know.
At our precinct, as in all our city precincts, there are separate books/rolls for Dems and Republicans during a primary.
Also, each table is divided into alphabetical lines, i.e. A-G, H-M, etc.
You stand in the appropriate line, the poll worker checks your voter ID and photo ID, you sign the book, and then they activate the card (electronic voting) with the right issues (in other words my screen only showed Republican candidates, not Democratic candidates.)