The Tim Burton Planet of the Apes not only makes sense, but I can put it in the same universe as the 2011 Rise of the Planet of the Apes (2011PotA), and the original 1968 Charlton Heston Planet of the Apes (1968PotA).
Spoilers to all follow:
The Ape saga starts with 2011PotA. In that movie, in the background of one of the scenes, we see the spaceship Icarus taking off on a news program on TV. That spaceship is taking Charlton Heston and the gang up on their journey. In 1968PotA, the spaceship Icarus hits an anomaly and is thrust forward into the future, arriving back on Earth which has been taken over by apes. This anomaly was just starting out and was in a much more chaotic state than later on. As such, Icarus bounces out of the anomaly without traveling very far in space, just traveling forward in time.
Meanwhile back on 2011PotA, for those on Earth, it appeared as if Icarus just disappeared. James Franco goes about his business of developing ALZ-112, which ends up making apes smart and results in a virus starting to spread around the globe.
Missing from a not yet produced sequel: The virus doesn’t wipe out humans, but does result in a huge global disaster with major geo-political consequences. While the smart apes are mostly wiped out by the government, many exist in the wild indistinguishable from others (when they don’t want to be discovered). The government decides it needs to conduct research and development so they can deal not only with smart apes, but other smart animals that might rise up against us in the future. A space lab is built so that no smart animals can escape and cause havoc on Earth again. Markey Mark is sent to space to work in the lab.
With Markey Mark in space, we have 2011PotA. The ape Pericles goes into the anomaly first. This is the same anomaly that sent Charlton Heston and his gang into the future in 1968PotA. However, now with the anomaly in 2011PotA, the anomaly is more stable, but still growing. Entering the anomaly sends you in a direction in space and a direction in time. The larger the anomaly the further in time and further in space. The anomaly follows a First-In->Last-Out (FiLo) process. Markey Mark follows Pericles into the anomaly and eventually the space station itself goes in.
Thus we have going in: Pericles->Markey Mark->Space Station.
Coming out: Space Station->Markey Mark->Pericles.
Pericles travels further into the future, while the space station doesn’t travel as far forward into the future.
So in 2011PotA, Markey Mark crashes on another planet after the space station, he gets caught, fighting occurs, Charlton Heston makes a cameo, he falls in love, all of that. Finally, while being chased by General Thade, he comes across the space station that crashed long before he did. More fighting, and General Thade gets trapped in the space station.
Then last to emerge from the anomaly, Pericles comes down to the planet without crashing. Markey Mark jumps aboard and takes off going back the other direction into the anomaly. Traveling the other direction sends you back in time and back in the other direction in space. In this case it takes Markey Mark back to present-ish day Earth. General Thade meanwhile survived, and was rescued from the crashed space station. He finds one of the probes and is eventually able to repair it and launch the probe into the anomaly.
Going into the anomaly after Markey Mark results in General Thade arriving on Earth before Markey Mark. Thus General Thade is able to muck around and distribute ALZ-112 that he was able to find and read about while trapped in the space station. Apes take over America with General Thade as the leader. Markey Mark lands at this point and sees Thade’s Aperaham Lincoln.
Missing from another not yet produced sequel: Humans in other countries go nuke, but due to the second wave of the virus and leadership by Thade, the apes take over Earth.
Meanwhile back on 1968PotA, the Earth that Charlton Heston landed on in the way distant future is the Earth that has been destroyed by humans and ruled by apes since General Thade.
All of this is documented by a message in a bottle found by two space travelers named Jin and Phyllis. Unfortunately, they dismissed all of it as humans obviously would never have the intelligence to write such a story.