Why would the Republican runoff be using the Democratic sign-in sheet? This just doesn't make any sense....
There are two poll books, each with a full set of names of registered voters. When a voter decides which primary he wants to vote in, his choice (or party) is recorded in that book.
In some precincts, probably not all of them, the election administrators used the DEM book, which identifies the people who voted in the DEM primary. This is a quick and reliable way (or should be) to prevent a person who voted in the DEM primary from voting the GOP runoff.