Go to minute 4:56 of film, where the title states that the present year is 2029, before ape domination.
Skip to minute 13:15 of film. Note that the years on the monitor of the space pod have skipped to at least 2472. Leo has time-traveled several hundred years into the future when he lands on the ape planet.
Fast-forward the film to 1:50:00. Note that the time labeled on the space pod monitor as the most recent year is 2155. Calculate that at least 126 years have passed since the year 2029 of the beginning of film to the new present day of 2155 when Leo lands back to Earth.
Skip to 1:44:39 of movie. Observe the close-up of General Thade hiding under the desk in the abandoned spaceship. Notice that he is last seen alive. This is to have us believe, though we don't know how, that Thade was able to time travel to Earth earlier than Leo and reverse the roles of apes and humans.
Rewind to 1:27:30. Listen to Krull's lines to Leo: "You don't understand Thade. He will keep coming for you. No matter what." This foreshadows Thade's determination to seek revenge against Leo.
Skip to the final scene of the film at 1:51:00 when Leo crashes into the Lincoln Memorial. Observe that General Thade is in Lincoln's place. Note that all of the officers and observers of the crash are apes. This proves that Thade somehow figured out how to reach Earth and overtake the humans.