Quoted from the last post of Kaspersky support thread above:
[User, then moderator]
"Well... the next day it did the same thing again. I actually clicked on a link on the popup tab and it did say "Hi, Androroid 4.1 user, there's an update for you..." and I clicked on that (full page icon of the Android icon) and it took me to the Play store to install the Dolphin Browser. It did ask me how I wanted to open the link, Play Store, Chrome Browser, CM Browser, etc. Each one of them took me to an in-browser Google Play Store page to install the Dolphin Browser. I installed it and that didn't do anything. I have no idea what the Dolphin Browser has to do with this problem. I highly doubt they have gone to the trouble of embedding code in some ad to trick people into installing their browser under the guise of an Android update.
So I'm guessing I just need to restore the phone to factory settings and re-install the apps I use (old school Windows days again). At some point I really was thinking I was patient-zero for some kind of Chinese government hack where they have taken over my phone, but now it just seems like some kind of bug in the Chrome browser mixed with an ad on Amazon plus older Android OS issues. The good news is that I have loved the help Kaspersky has given plus their software. If my phone ever does get stolen, I can at least get a mugshot of the fool who wanted my cheap phone.
Okay yes could be bug in Chrome browser before you installed Kaspersky.
Try this before you do a Device factory reset.
Settings>Application manager>All>Chrome>Clear Defaults>Clear Cache>Clear Data>Uninstall Updates. (restart device)
After restart go to Google Play Store re-install Chrome.
Open Chrome sign in to Google.com, close chrome then re-open and see how Chrome is working.
Go to Kaspersky settings>Web protection>re-set Chrome as default browser.
If none that works do as you said a Device factory Re-set."