I believe this is happening due to the fact that on the web client, document loading is throttled, which means that searching everywhere has to wait for every document to load before displaying accurate results.
One improvement we could make in the future is to have it show up with some results first with a loading bar or spinner, and as new documents gets loaded populate the page with results.
Alternatively, I would suggest you to bookmark (not the browser bookmark) your search everywhere result page and use that to navigate without triggering a page-refresh. Once all your documents are downloaded, search everywhere should be almost instant.