A run works out the phrases, looks up who ranks for them, checks search volume with Apple, measures the category, and writes the summary. Each of those ticks over on screen the moment its own work is done.
Refreshing mid-run is safe and costs you nothing. The work happens exactly once per report however many times the page asks for it, so a second tab or a browser retry lands on the same finished report.
If a phrase in your report is one we have never looked up before, we go and fetch it immediately afterwards — so a search showing no results at first may have them a minute later.