Characters Randomly Appearing When They Aren't Supposed To

Greetings!

I've built out a complex slide with multiple characters fading in and out of the slide. When I preview the slide and select "Play," the slide animations, transitions, and triggers work out perfectly from the beginning to end.

However, if I were to drag the timeline to an earlier or later starting point, some of the characters will randomly appear in scene, even though I have them programmed to only be in a certain timeline of the slide.

What am I doing wrong? Is there a trigger or something else I should be doing to make sure they don't appear when they aren't supposed to?