I own red eared slider turtles, while not exactly exotic it's funny that the three things they are known for by owners are things normal folks would not expect.

1. Turtles are escape artists. Because they need so much water to swim in and need basking areas, you'll generally want to fill your tank up as high as you can, and then have a basking platform up there. They will use those and filters to try to escape. They may succeed. There are a ton of questions/guides online to address this https://www.youtube.com/watch?v=QHbV5nsDCb8&ab_channel=TheTurtleGirl
2. They are destructive. You will want to have a filter for them, and they will attack the filter with the fury of a bored creature attacking the thing making a noise. Many filters will fall to their wrath. If you google it you'll find ton of stories of turtles destroying filters/water heaters. https://www.youtube.com/watch?v=cnD3cKuFOa0&ab_channel=HMoore
3. They smell. How can such a small creature smell so powerfully? Magic.

Any other pet owners have secrets about their type of pet?