There's Auto tone in the Basic panel; there's Auto WB; there's As Shot WB; there's Upright; and OTOH there are the particular settings resulting from having used these controls on a particular image.
Lightroom has several methods to "spread processing across" multiple images, and these can operate differently (between these respective methods, and also between LR versions for the same method) so far as HOW those auto modes / settings will get treated.
There's Auto Sync, there's Copy/Paste, there's Sync, there's Previous. There's Develop presets, which include an optional Auto checkbox. And there's Set Default for a given camera / file type / optionally ISO etc.
It's more complicated than one single simple answer can cover, so the best advice is indeed Just Try It. 
- You may sometimes want the fixed RESULTS from the processing of one image, however achieved, to get copied onto others -.desiring those identical slider values because of what you want to then do with those pictures (compositing / stop motion / whatever).
- You may sometimes want the FACT of such a mode to spread between pictures, such that each one is processed according to the same general intention, doing so via differing slider values depending on the capture and the picture content.
AFAICT the trend over successive versions of LR has been more and more towards delivering the latter sort of outcome.
So if you want to get the former sort of result, you can "trick" LR by changing something (which is within the scope of the Auto tool) and then changing that back to the same value. This now shows up as Custom / Manual processing rather than as Auto processing, and that is what then gets copied over to other photos.
In the case of the Auto tone in Basic, whenever the Auto title goes dark and inactive, auto processing is already in place and the FACT, not the RESULTS, of that is what Sync (etc) will then use in latest LR version. When the Auto title becomes bright (an active button) this denotes that you are currently dealing with non-Auto processing.