I messed up somewhere with multi-user functionality of my Android 5.0 ROM and because of that the following method was tested only on stock Android 6.0.1.
The owner has root access while the other user doesn't So I can't use titanium as the other but I need to make backups of the other user's apps. (sic)
SuperSU supports multi-user functionality. In its settings you would find the option Enable multi-user under the section Security. Enable it. When you would attempt to enable it, SuperSU would show a dialog stating that all users need to have SuperSU installed in their account and the way to go is to have SuperSU installed as a system app.
Make SuperSU app accessible through every user account
It's very simple to do using ES File Explorer. Copy the apk of SuperSU into /system/app/, reboot and you're done making it a system app.
Alternatively, you can setup adb in PC and execute this command:
adb install -r FILE # replace FILE with file path of latest and stable SuperSU apk downloaded in your PC
-r would (re)install the app in all the user accounts.
If you've a terminal emulator app and apk available under /sdcard, then you can execute this command:
pm install -r FILE # replace FILE with file path of SuperSU apk wherever it is available in /sdcard
Do the same with Titanium Backup app's apk as well, or alternatively, you can always go into that secondary account and side load the app (I doubt whether a secondary user is allowed to do that).
Protect SuperSU from unauthorized access
Protect your SuperSU app with a PIN code so that nobody can grant root access to any app without entering that code. You need to set PIN code in SuperSU when you're logged in as the owner. The PIN code would apply on all user sessions.
You can set PIN code from settings of SuperSU app. It is available under Security section.
This would cause some (major) inconvenience to you since even when logged in as the owner in primary account, if an app demands root access you would be given the option to grant the access only when you enter that PIN code. That's the price you've to pay.
Set Default access to Prompt in secondary accounts
In the SuperSU app of your secondary account(s), make sure the Default access type is set to Prompt only.
Time to launch Titanium Backup in secondary account. Titanium Backup would look for root rights and you would be shown a window by SuperSu to provide PIN code. Provide it, grant root access and that's all to be done for setup.