Can application be installed on an Android phone without confirmation, just by visiting or clicking links on page?
The app can be automatically downloaded, however Chrome does warn you before downloading an APK file. So, that's check one.

Next, any app package (apk) which you try to install outside of Play Store requires your consent before the installation is started.

And you also need to enable "Unknown Sources" before such an app can even start the installation.

So, going by these checks, yes the file can automatically download on your phone. But I'm not buying that it will install automatically as well. Your phone should be clean right now if you haven't installed the app.

Just check your downloads and remove any unknown APK package that you see. Thereafter, start using your phone normally without worrying.