Just to confirm. When adding bold, italic, underline tags you immediately press back-arrow (as backspace would delete the words since the area is highlighted). It then traverses left till it finds a ']' bracket and then jumps to the right most bracket '[' on the second back-arrow. It only does this in 'edit' mode. On my system Firefox v25 did the same thing. Note: you do not actually see the brackets since it is in editor mode, but pretend they are there per this example.
Can you confirm this is what you are seeing?
Not quite. I'm not talking the back arrow but backspace. Say you're typing in bold, italic or underline and make a mistake and need to delete it, the cursor jumps back. I'm linking to a video capture to highlight what I'm talking about.
Also, I'm running the latest version of vBulletin. I've also tried disabling all my plug-ins and using the default vBulletin style. Neither of these things resolve the problem. vB support seems to think it's a CKEditor bug.