I have several games with web versions, and whenever I’ve updated them, the update is reflected instantly on Itch.
In all my years on Itch, yours is the first and only case I’ve heard of involving this specific problem.
For that reason—and I’ll say it again—I’m almost certain the issue is on your end; however, years of working in IT have taught me that no matter how sure you are about something, it’s always best to double-check.
Add a text element to the game that displays the version number so you can quickly tell which version you’re playing. Make sure you’re uploading to the correct channel and that you aren’t playing a version stored in a local cache on your machine.
If, after testing and ruling out all potential issues on your end, the problem persists, your best bet is to contact support with all the relevant technical details—because if it turns out to be an Itch-side error, it would be a significant one.
I suspect that, somewhere along the line, a cache is causing you to play an older version of your game.