The origin of the phrase, “Tile the doors,” likely came from 18th century Freemasons who called doorkeepers “tilers” or “tylers.” To “tile the doors” meant to guard a secret Freemason meeting from outsiders by posting a tiler at the door.
Who knows how labour unions came to adopt the expression, but they maintain the practice of posting people at doors during secret-ballot voting to limit people from going in or out of the Convention hall. The practice has more to do with protecting the integrity and fairness of voting procedures than with keeping outsiders from discovering a secret organization.