himbim That's not normal. Once you tap that notification it should show a 'install' dialog to allow the update. There is absolutely no need to log into the Play Store for this. That login screen is probably the Play Store homepage that is shown by default instead of the intended update confirmation dialog, presumably because of a bug or configuration error.
Have you granted Play Store the permission to install unknown apps in system settings? If you haven't, it might be that the update confirmation screen cannot be shown because of this. You can enable it and wait for another notification. Please try it and tell us if it solves the problem (or not)!
himbim Is there a way to post screenshot actually?
I don't think it's currently possible to attach images directly on this forum. The easiest way is probably to upload an image somewhere else (imgur or imgbb for example) and link to it here.