How long does it take for iCloud to update my password on other devices?

I setup a new apple ID as an administrator account for multiple new macs we received at a non-profit computer center for our retirement community. I successfully created the account and can log into/out of it on the device I created it from just fine. On ANY other computer (Mac or PC) it tells me the password or email account is bad; so I changed it...

Again, it works with the icloud account I created ONLY on the device I changed it on. All other Apple or even PC computers if I try to log into iCloud with that newly changed password and icloud email address tell me the password or user ID is bad. It seems like there is an extended delay in updating iCloud's password/user ID database - it is apparently not immediately changed when you change it on a device.

So how long is the "lag" time? How long do I have to wait after changing an iCloud account password before that change is recognized when logging on through any other device than the one on which the change is made?

[Re-Titled by Moderator]