I believe that the esp module goes to the internet and gets time from an ntp server every time you execute the time() function. (but I am not certain )
This would be a good place to use the wireshark tool (I believe it can do wifi also) to see what the esp module is doing when you do a time() get.
If you haven't heard... wireshark is a free opensource "excellent" network sniffing tool.
I have not used it a lot but it is pretty easy to filter on either a mac address or an ip address and then you could tell if the esp module was accessing the internet every time you do a time()
In one of my Seniors moments I took the easy way out and asked on the forum instead of thinking the issue through and looking at the network traffic on the screen. Anyway, wireshark installed and the secrets of the net traffic are being revealed.
No problem on the late reply.
Please report back here what you find.
Many of us have the same questions.
I am working on a program that I would like to keep track of time and wonder when the esp module actually goes to the internet to update.
My assumption is every time it encounters a bla = time().