I can see that there’s something wrong in your nice screencast, but to find out what that is, and to fix it, I’d need to access the page directly.
Can you therefore please post a link to the page with this table?
thanks for the link.
The reason for this problem seems to be some weird CSS in your theme, which changes the padding around table cells when the mouse moves over them. To fix this, please try adding this to the “Custom CSS” textarea on the “Plugin Options” screen of TablePress: