How To Diconnect A Tp-link Td-w8951nd Modem Router On A Bsnl Connection

Greetings fellows,
So I need help with this problem. I am on BSNL night unlimited(2-8 am free) connection which I connect to using a TP-link TD-w8951nd modem router. My question is - if I turn off my computer, does the internet connection automatically diconnects or not? I use night time for heavy downloading and don't want to be to be hit with massive bills. I could use the bridge mode of modem to connect to internet but it is very very sluggish and some sites fail to load on that mode.
From what I am assuming your connection would still be on. I think with BSNL broadband connections it connects automatically when the computer is switched on is that correct?

But to be on the safe side and if you have doubts, just switch off your router as well.