Making a movie can be difficult. Sometimes, twisting or stretching reality is necessary to make the movie more entertaining, but to counter that, there's the concept of suspension of disbelief. Suspension of disbelief is when the audience is still able to enjoy the movie because they can willingly ignore the lack of realism. Certain things, such as plot holes, implausible explanations or that which offends one's religious views, push suspension of disbelief too far, and the audience ceases to enjoy the movie.
In the Jurassic Park/World franchise, the majority of dinosaurs have been modified so that they look and behave differently than their real world counterparts would. There is even a canonical explanation for this: The DNA used to clone the animals was incomplete, and thus had to be filled in with the DNA of other animals, mostly frogs. These differences, while rather annoying to more educated dinosaur fans, are not so major that most audiences would find it difficult to enjoy the movies. This is because it is somewhat believable, and even has an explanation built into the movie.
One thing that would spoil the movie is if the t-rex somehow possessed teleportation powers. This ability would push the audience's suspension of disbelief so far that many of them would just switch off at that point, or at least stop taking the movie as seriously as it tries to present itself. It's just not realistic for a dinosaur to be able to teleport, no matter how much foreign DNA you put into it. It takes too much imagination.
Although Evolution is extremely unrealistic, it is so heavily ingrained into our culture that it can be safely included in the movie without causing too many problems with the audience. But though it is within the realms of suspension of disbelief, it barely touches the border. It is a twist of the truth designed to appeal to the religious beliefs of the audience, the majority of whom probably believe dinosaurs died out millions of years ago. Just like the incomplete genome explanation, there is an explanation for the millions of years thing. In our modern world, dinosaurs seem to be completely extinct. Even within the past 2 millennia, dragon legends have become increasingly rare, suggesting they didn't last too long even after the flood. Their absence in the modern world, and their prominence in the fossil record, means it is easy to convince an audience that they went extinct before man came to be.
As easy as it is to convince an indoctrinated audience that dinosaurs have been brought to life after millions of years, there is much evidence in the real world that precludes such an extreme age of dinosaurs. For example, it is common knowledge that soft tissue does not last very long, even under the perfect conditions. Current estimations suggest that even the best preservation methods could not preserve soft tissue for more than 2 million years, way below the > 65 million year age given to most dinosaur fossils. And yet, soft tissue is occasionally found in dinosaur bones, to the point where they are sometimes mistaken for modern bones.
Another thing which has been found inside dinosaur bones is Carbon 14, which should be undetectable after around 50 - 60,000 years, again being significantly younger than Evolutionists say dinosaurs are. This problem also occurs with diamonds, which also supposedly take millions of years to form.
Aside from scientific evidence, there is also historical evidence that dinosaurs and man co-existed. Dragon legends, for example, are very common in every culture worldwide. Despite the isolation of their respective cultures, these are often very similar, and have details that realistically describe dinosaurs and their ilk, even better than paleontologists initially did. Due to this phenomenon, Carl Sagan actually proposed the theory that memories can be passed on to our offspring (1). His idea was that because our ancient ancestors did see dinosaurs, our less than ancient ancestors "remembered" them, and that's what caused the legends. This, again, pushes the boundaries of suspension of disbelief.
But the most reliable historical evidence that dinosaurs and man lived together is the inerrant word of the God who created them. In Genesis 1, we find that the entire universe was created in just 6 days, with man being the final thing created on the 6th day. Land creatures, such as dinosaurs, were also created on the 6th day, meaning dinosaurs were created no more than 23 hours before mankind. Further evidence comes from Job 40:15-20, in which Job, a seemingly ice age figure, was told by God Himself to observe a huge creature, the "chief of the ways of God". This creature was a large herbivore, and special attention is paid to its tail, which moved like a cedar. Although the precise identity of this creature, known as "Behemoth", will likely forever remain inconclusive, its description fits large dinosaurs, such as the sauropod, far better than any other animal the world has ever seen, including the elephant and hippo, which certainly do not move their twig-like tails like cedars.
Interestingly, there is even some suggestion that God planned to wipe out these massive creatures. In the description of Behemoth, God explains how He, and He alone, can approach Behemoth with His sword, a phrase which usually denotes a judgement from God, and Isaiah 27:1 speaks of another large reptile, this time a sea serpent called Leviathan, that God will punish and cause to flee. Based on the description given of this beast in the Bible, many scholars believe Leviathan to be a crocodile, which is certainly a possibility. However, there are some distinct features Leviathan possessed which do not fit modern crocodiles. The most common identification proposed by ministries such as CMI is the sarcosuchus, a huge crocodile with tough skin and a bulbous nose (2).
With all the available evidence, it's clear that the extreme ages assigned to dinosaur fossils are nothing more than the wild imaginations of a secular religion, specifically designed, as Charles Lyell once said, to "free science from Moses". In reality, dinosaurs and their ilk are just more animals God created to reveal His glory to the species He designed to bear His image. To say dinosaurs ruled the earth is no more accurate than to say that in the beginning, the Indominus Rex created the heavens and the earth.
References
1. Sagan, Carl - The Dragons of Eden, 1992
2. Cosner, Lita - Leviathan - Real or Symbolic, Creation.com, December 2013 (link)