This weekend I installed a popular Windows antivirus in my PC laptop. The installer offered the android app, and I denied it.
Nonetheless, a couple hours later all my android devices had the antivirus' app pushed onto them, even the ones that were lying around unused for a week.
It means that none of the devices (three tablets and three phones) were ever connected to the PC in the previous or following days. And the installation notification for the antivirus app had Google play's icon.
I haven't order the download of the antivirus from the play store to the devices.
It seems the antivirus software or its installer did it from the PC. I have several google programs (drive, chrome, etc) installed on the notebook.
Due to Moderator request, the name of the antivirus is Avast free.