what is the personality of Travis?

Travis is one of the safari guides, and he presents himself in a way that is reminiscent of a former military man. He doesn't waste time with small talk or pleasantries. He also isn't shy about "telling it how it is." He is straightforward and to the point about time travel, its risks, and his expectations of each of the men going with him to hunt the dinosaur. He gives information to others that is necessary for a successful trip. Travis knows that what they are doing is dangerous and that screw ups could have huge repercussions. That's why he is so emphatic that the men stay on the path.

"Stay on the Path. Don’t go off it. I repeat. Don’t go off. For any reason! If you fall off, there’s a penalty. And don’t shoot any animal we don’t okay.”

Travis holds himself to a high standard of excellence, and he thinks other people should do this as well. He has very little patience or tolerance for men like Eckels. This becomes clear once Eckels makes it clear that he doesn't think the death of a single mouse is that big of a deal.

“So they’re dead,” said Eckels. “So what?”
“So what?” Travis snorted quietly.

Finally, Travis is a man that believes in quick and immediate judgment/punishment. It's not clear if Travis shoots and kills Eckels or himself at the end of the story. He's either punishing Eckels for stepping on the butterfly, or Travis is making sure that he (himself) doesn't have to answer to the authorities. Either way, Travis makes an immediate and final decision based on what has happened.