Purple dot near app which downloaded by iCloud sync I added my account to my old iPad mini and I downloaded this app on it. Then, I used my iPhone and saw that the app downloaded too on it. Is the purple dot DOES mean that it downloaded by sync? And can I shut this feature off?
A blue dot before an apps' icon name means that it has not bee run yet (or it is a new version that has not been run).

An orange dot means that the app was downloaded as a beta as installed through Testflight.

The last is from this SO answer which also suggests the colours alter if on a different background.

Try a plain black or white background to see if the colour changes to one of these known ones.