No, Android doesn't "get severe viruses" or malware much; it's Linux based, and is generally quite secure from being exploited even if a user does manage to install a malicious app. And while it is possible to get it from a website that uses an exploit on a mobile browser, it is extraordinarily improbable. Most likely the AV is reporting non-malware like tracking cookies as "threats".
AV companies define "threats" extremely broadly, in order to keep users paranoid and buying their software. One of the ways they do this is to include things like tracking cookies and the like, which aren't technically malware. This is probably what your AV is "detecting", as website drive-by malware infection on Android is hugely unlikely. AV for the average user is useless on Android (and worse, slows down your phone); AV providers prey on user ignorance and fear from the fact that Windows requires AV (which most users have had drilled into them by now) to sell their products for Android.
The most likely scenario for getting malware is installing an app from someplace other than Play (sideloading), followed by being incautious when installing a Play app and not bothering to check the permissions an app is asking for (even then, extremely unlikely that it could do much other than send some of your personal info to a server for marketers to buy, or use up your bandwidth to pop up ads).
Many malicious websites will start automatic downloads, in the hopes that you'll be foolish enough to run whatever is being downloaded. So long as you don't install whatever it is, there isn't a problem.