Or is the router doing some packet filtering or something along those lines without me knowing
A router does NAT and that means no incoming connections being made from the internet to your public IP will ever reach the machines inside your network. They'll simply be dropped / ignored. Only if a machine initiates a connection then a response from some server on the internet will be forwarded to it. Because of this NAT is in itself a very solid firewall that protect your computers against threats coming from the internet.