Time capsule shared disks users account issue with time machine

Yes,, I would NOT use "With Accounts"

It is not achieving anything other than making your life difficult.

Simply go back to using default i.e. same as admin password on the Time Capsule.. or if you want added security you can use a disk password.

With Accounts makes no difference to the backup.

(If I use another user/password setup from a different iMac it works fine but then it's using the same backup (image disk I guess ?) partition is for both iMac... which I don't thing is a good solution for recovery.

No.. this is not the case..

There is no partitioning..

Each Mac creates a backup image called Sparsebundle. It is a virtual disk so acts somewhat like a partition. So it will never mix backups.. indeed it cannot do it.

You will simply have two Sparsebundles under one account and a third one under another account.. all go to the same partition.

Using identical username and password on two different Macs will in no way change the operation of Time Machine. It will produce separate Sparsebundle for each computer.

It will stop anyone without the username / password from seeing the backup. Which is absolutely pointless. It offers no security at all.. because anyone can simply press the reset and change the setting.. and recover all the passwords.

If you want the backup secure encrypt it via the setting in Time Machine. But leave the TC running with device password.. which is default.

People very seldom use the user account method of access.. from past experience it does not work very well and it is dead simple for someone who wants to get around it to do so.

Perhaps you can tell us what you are trying to achieve with user account access.

As far as network is concerned.. on the Mac that has issues, does the TC show up in Airport Utility.

If so,

Can you mount the hard disk in Finder?

I can only guess what the original intent was.. probably increased security.

Encryption did not come until Time Machine update in Lion. Before then anyone could access your files from Time Capsule.. so with accounts added some very minor security improvement.. but mostly for the sake of the end user concerns.. it was still hopelessly flawed by the soft reset if anyone had physical access to the TC.

Otherwise it may have been intended to set actual disk limits.. ie each user has a set size limit.. which would have actually been useful. Apple did introduce this with Time Machine functionality in server extensions.. but it never made it to the TC as independent function.

Apple tend to update firmware but change only items that are problems.. since it was there.. they just left it in.. but user base learned not to use it.