* https://www.kayak.com/flights
* https://www.google.com/flights/ ($$$)
* https://www.hipmunk.com/ ($$$)
The ones with the dollars signs were the most expensive. These sites are not all equal some are more reputable than others, etc.
In addition, the "proof" provided on that subreddit has quite a few problems:
A) That route is priced ridiculously anyway, and they are looking at Delta, who always price ridiculously. Delta doesn't care about price-conscious shoppers, so they have virtually no incentive to try and segment fares based on browsing history, etc.
B) They're looking at a third party flight aggregator. These are the WORST ways of buying flight tickets. They're decent for _finding_ deals, but 9/10 times, the airline's website sells it cheaper, and the airline's website gives you more benefits anyway (as you're the buyer and/or owner, not the online travel agent).
C) Furthermore, these online travel agents cache flight lookups _very_ heavily. My guess is that the search with TOR routes to a different edge server with a different cache. API calls to the airlines are extremely costly.
The best way of getting a cheaper flight has nothing to do with your browser, so don't worry about it. The best ways of saving money are based on _when_ you buy, and of course what airline. Don't buy on a weekend, and try not to fly on one either. Holidays are similar, except it's not a bad idea to actually fly ON a holiday, but not around one.
Note that most of them won't offer the free 24-hour cancellation required in the US for airlines, and I have heard about problems with tickets sometimes not being issued correctly, but I have used whichever OTA happens to be the cheapest when I'm booking and have never run into problems.