Among the details long since forgotten, on that day in 1966, when word first started to go around the campus about a man firing a gun, few people knew where, or in which building, he was located.
In the student Union Building (perhaps elsewhere as well), a rumor was circulating that the gunman was on the top floor of the Union Building and was working his way down, shooting people as he went.
No one in the Union Building was armed; no police of any kind were present. People suddenly realised, with at least some shock and horror, how defenseless and desperate they were if the rumor proved true. And the gunshots were audible, even indoors, although I suspect that someone experienced with shooting would have guessed, from the sound, that the shooter was likely further away.
Within about ten minutes of the rumor's circulation, most people inside of the Union Building fled outside, in other directions, with some undoubtedly walking directly into Whitman's line of fire, as that was the direction immediately facing the main entrance/exit of the Union Building in 1966. (if Whitman had been on that side of the Tower at the moment in time, which is something we'll never know).