Neither the elections official, any member of a precinct board, nor any other person shall count any votes, either for a ballot proposition or candidate, until the close of the polls in that county. After that time, the ballots for all candidates and ballot propositions voted upon solely within the county shall be counted and the results of the balloting made public. However, the results for any candidate or ballot proposition also voted upon in another county or counties shall not be made public until after all the polls in that county and the other county or counties have closed. This paragraph applies regardless of whether the counting is done by manual tabulation or by a vote tabulating device.