The caching of favicons, I have found in my times as a web developer, is a mystery. I've found that (if the favicons are correctly linked and updated) it might take your browser a day to update. When I'm in doubt, I hop onto a coworker's computer that has never visited the site and see if they work on that fresh machine.
So long as they're coded correctly and uploaded correctly, I wouldn't be too stressed out if they don't load immediately on your own computer. Rely more on fresh computers which haven't visited the site.
If you have questions about whether they favicons are coded correctly, you can post the link to the landing page and I can check out the code.
Best,
Edward UnthankMarketing Operations Specialist
Yesler