Hello, AlEx and thank you for giving Total Suspender a try!
First of all, since addons reviews page does not allow for a conversation (I can only give a reply), I would like to request that you create an issue on project's github page ( https://github.com/k5md/Total-Suspender-webextension/issues/new ) to make communication more effective.
To save your time, please, provide your settings in issue (especially "Ignore tabs producing sound" option status), and try to disable automute and if it doesn't help, disable Open Tabs Next to Current?, so that we can find out what causes the problem, since that if other tab suspending addon doesn't work, it is highly likely there is some conflict with Auto mute extension (then, updating tab state to "muted" somehow changes it's "audible" property?), or with tab-moving "Open Tabs Next to Current?".