Minecraft – If I wanted to take a cat over an ocean, would it teleport behind the boat

Mob traps built close to the sky limit have been known to end up not being completely loaded by the engine in some situations. The way to test for this is to open the F3 screen and look at the 'lc' value. This number is the highest Y-level that is currently loaded. If it's lower than the top of your mob trap then you would need to add some blocks above the trap to force the entirety of it to be loaded. This youtube video shows how you can fix the problem if it happens

It's also worth mentioning that the high altitude mob traps are (all other factors being equal) always going to be at least somewhat slower than low altitude mob traps simply because there ends up being more blocks for the spawning algorithm to check

This might have something to do with the server render distance/your render distance. If the render distance on the server/client is too low, then it's likely that the cats won't teleport to you.

The cats might also be sitting. Right-click on them to make them not sit and (hopefully, if your server/client isn't just plain broken) teleport to you when you get far enough away.

Also, if you'd like your pets to go through a nether portal, you should have them stand in the portal fluid to teleport them there, then you got there, then you're all in the nether by your portal!

Unloaded chunks can cause pets to freeze. This is what happens when your render distance is set too low. If you'd like your pets to teleport to you while you're in the nether, have someone stand close enough to your pets to have their chunk rendered so they are able to teleport to you.