Hi Lars,
Where are you setting up the subscriptions? The Teams publisher is different to most as it only allows publishing to a single webhook URL. There is no ability to set a recipient username or channel so subscriptions can only be set up on the Administration -> Subscriptions page, not on the Subscriptions page under the users profile.
By default, subscriptions set on build events will send a notification every time that event occurs for the selected project(s) or configuration(s). This is independent to the user who authored the commit.
There is, however, an option on repository triggers labelled “Only notify users who caused the build”. If this option is ticked build notifications for builds started by this trigger will be restricted only to the user associated with the triggering commit. Can you check if this option is switched on?