Immediately after switching the page, it will work with CSR.
Please reload your browser to see how it works.
(like me for your question, as I never tried TabSub with internet disconnected. Was delighted to see it works nevertheless)
You can try on the demopage when you
1. play the songs each (for them to buffer a little audio snippet)
2. open the page in a second tab
3. Disconnect from the internt
Still works :D