I had the same pop-ups recently. The only way I found to stop it (except root) was to install "NoRoot Firewall" and deny access to "download manager" (and many other apps, of course).Not yet unfortunately. Currently I'm experimenting by turning off that "Draw over other apps" option, turning it off for 1 app at the time and waiting to see if it will stop. But it's like that damn malware knows I'm trying to figure it out. Before I started with that last few days it was showing up like 20 times a day. Since I started it sometimes even goes a day after I turn off some app before it shows up again.
I believe it is actually downloading and installing apps to our phones. When you see the pop-up, check the following folders with a file manager:
>root>sdcard>.adslib
>root>sdcard>.androidsystem
>root>sdcard>Download
You will see that installation files (and icons) are being downloaded in these folders. So after deleting them manually many times, I installed NoRoot Firewall and the problem stopped. (you just need to unblock download manager when you want to update apps and then block it again).