Follow up: I added a tag in the gallery with the AMM uninstalled and it worked. I then re-installed the AMM and tag remained. I was also able to remove and reselect the tag. So I'm sure you can replicate the effect. However, on initial install it would not show the tags.
This is probably caused by something weird in the XML file of that module.
Can you give me (super) admin and (s)ftp access so I can take a look?
You can use the 'Confidential information' button in the forum editor to hide sensitive information.
Also, the plg_system_web357framework is causing a javascript error, as it is referencing jQuery, but not making sure it is loaded.
Can't really tell why it is loading a different Tags field.
But this module is using old Joomla style coding. It is not using namespaces, and not using prefixes.
This can cause conflicts when other fields with the same type/name are being loaded.
I tried to reproduce the issue on my setup using a similar old syntax, but couldn't replicate it.
Either RS should update their code, or it simply means it is not compatible with Advanced Module Manager.
You'll have to choose which extension you want to use.