Toiletterider Which system app is making the connection to sync time? It is not stated in the link.
It's not 100% clear that it works that way.
The explanation for the "Automatic date and time" toggle is "Set automatically using your network and wireless signals". So it is possible that one piece of code runs when the cellular network becomes connected and a different piece of code runs when a Wi-Fi network is connected. It is also possible that neither of those pieces of code is an "app" that shows up in Settings.
The HTTPS time client code appears to be in frameworks/base/core/java/android/net/HttpsTimeClient.java, and it appears that there is code in frameworks/base/core/java/android/util/NtpTrustedTime.java to force the HTTPS code to be used instead of the NTP code. The fact that those are framework classes does suggest that multiple bodies of code could invoke this code.
I've looked a bit and nothing is leaping out. Maybe I'll look more later, or maybe somebody else will chime in.
Meanwhile, can you confirm that the "Automatic date and time" toggle is on?