This sounds like a bug, the input should be focused right away once you open the popup.

I know at least one other user raised the point https://github.com/reblws/tab-search/issues/13 here, but I'm having trouble replicating it.

Could you let me know you browser version & OS? You can also contact me by email or that GitHub issue (if you have a GitHub account) if that makes it any easier for you.