Travis and the other safari guides have strict procedures in place that have so far worked to keep the present/future safe. I think the most important procedure that they have in place is the education of the men and women that are traveling back in time. Travis and his coworkers make it clear that traveling back in time is no joke. It is serious business and messing around with the time stream can have massive repercussions. Eckels doesn't see the point, and the guides explain in further detail using the death of a single mouse. Travis goes onto a step by step list of repercussions that comprises one of the story's longest paragraphs. The single death of a mouse leads to a future in which the United States doesn't exist. Eckels says that he "sees" the point, but it is still him that crushes the butterfly and changes the government of the United States at the story's completion.
The safari guides are not so ignorant that their little education lesson will prevent all possible mistakes, so they have other procedures in place to help make sure no historical changes happen. The time travelers are forced to walk on a path that stays hovering above the ground so that the men do not so much as bend a blade of grass. The dinosaur being killed is one that has been identified as going to die within a short time anyway. Bullets and casings are retrieved, so they are not left in the past too.
"Then I correlate our arrival in the Past so that we meet the Monster not more than two minutes before he would have died anyway. This way, we kill only animals with no future, that are never going to mate again. You see how careful we are?"
I do also think that an intentional procedure is a scare tactic too. From the very beginning, the safari guides do mention the dangers frequently enough to sober the cavalier attitude of men like Eckels. The safari guides do not want or need careless bravado of paying customers.
Eckels flushed angrily. "Trying to scare me!"
"Frankly, yes. We don't want anyone going who'll panic at the first shot.