You are right, no wifi, no control.
But he said internet connection down.
So wifi signal is never down. 
I normally connect with my mobile to do it. Give the hotspot the same name and pwd. It works. The signals are weak.
Even after connecting the SDA and SCL to A4 and A5. It is not working.
Any help here? I really need this, Even yesterday the light didn’t on due to the server sync
Sorry, I can’t help, I never use RTC module as I use NTP server.