Is it strange that we want a person dead just because we're afraid of them?
No, it's not strange at all. If you're afraid of someone, you have to take them out. That's not weird in the slightest.
As Yang Yi and Jethro talked on their way, Yang Yi gained a comprehensive understanding of Big Ivan; Big Ivan evolved from a mere name, a concept, into a living person.
Once they got back to their base, the first thing Jethro did was announce a reward.
Protecting the employer is the bodyguard's duty—it's only natural for them to handle certain tasks, and it's not typical for a bodyguard to be rewarded just for doing something. But this time was different; if Trident hadn't protected Jethro under extremely unfavorable conditions, Jethro would have been in big trouble.
If Jethro knew how to be a good boss, it would only make sense for him to show his appreciation, and that's exactly what he did.