In Chrome, try to force refresh (Shift + Ctrl + F5) several times in a row to see if the changes become effective.
From what you explained, I'd suspect an issue with your hosting service/ISP or maybe your NAT/network parameters since when you host locally, browsers have no issues.
You don't tell what is the OS of the people who have issues seeing the new versions. This may be something to look into too.
Also are you sure when you update your file that you follow the process indicated in that tutorial ? (uploading again/overwriting the old offline.appcache)
You might want to check out if the issue is there with the mentioned event "Is downloading update". Do a debug version in which you display the value of this file to see if the target client is "aware"/downloading the newest version.
If it is not, it might indicate the newest version isn't "recognized".
I hope this helps.