And yes, your little router, is actually a router. It will dutifully take packets from one interface, look at it's routing table and figure where to spit it out. That's what it is supposed to do, NAT just adds a rule that says if a packet comes from eth1 and is destined for 0.0.0.0/0 (default route) out interface eth0 then we (the router) want to masquerade as if we are the source of that packet, so that this entire network looks as if it is coming from one single IP.
No firewall involved, and packets arriving on eth0 are going to get routed to eth1 all the same, since after all, we are a faithful little router.
This is how routing has worked since the dawn of time. Adding a firewall means we can say "but I should never see traffic destined to 10.10.10.0/24 on eth0, so drop it".
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Either way, NAT may be part of the firewall but there is no requirement for it to be part of the firewall. When it comes to IPv6, just like IPv4, a firewall is required, and as soon as you have a firewall that blocks incoming traffic, then NAT becomes meaningless.