Truthfully I can not remember, I have questioned this myself some time ago but that might have been in connection with the Fly App, either way I can not, at the moment, find the post. I like my DAT logs (see below "1)") plus I do not like the idea of my flight logs being in someone else's control so I do not want syncing to take place.
I think syncing has to be authorised so one solution might be to uninstall the App and then reinstall it. That might mean that syncing is unauthorised. If you do not want to change the app version download and install the APK for the old version from one of the APK sites. I am on the wrong computer to check which APK site I have used.
When you look at the flight logs in the App there is a cloud like symbol at the top right of the page, there is something in my mind about that but I am reluctant to experiment. I also had a browse through the gear cog / settings thing there's rather a lot authorised in that but where it reads "DJI " I am uncertain whether it refers to an internet connection to DJI or allowing the App and only the App to access data from the phone.
I can think of two possible ways to check if you are syncing flight logs, fly a flight and
1) Using the phone's file browser check your phone for a corresponding DAT flight log. I believe syncing deletes them.
2) look at your avatar? thing on the DJI forum (the DJI site, not here) and see if the flight distance thing increases.