Hi, I didn't misunderstand anything, one thing is what it should do and another what it actually does - what I wrote are my experiences with rutx09. I have it connected to linksys wrt1900acs running openwrt.
Bridge mode - when received private IP (modem is not connected yet), it will not change private IP on wrt1900acs until dhcp lease expires and internet connection does not work - this is a bug and dhcp should not be enabled at all in bridge mode, when I manually turn off dhcp server in bridge mode, I won't get IP from ISP. Also, when I receive ISP IP on my wrt1900acs, I can still connect to rutx09.
Passthrough mode - when received private IP (modem is not connected yet), it will not change private IP on wrt1900acs until dhcp lease expires and internet connection works, because it does NAT.
Also, every time, I change bridge/passthrough/NAT mode, I need to restart rutx09, because it behaves strangely (I can't remember exactly, when I was testing it, something like it worked with private IP in bridge mode when I changed from NAT etc..)
"I have tried to replicate the issue of DHCP assigning LAN IP when using bridge mode, but everything worked just fine. Could you provide me steps on how to reproduce it? " - in my case, what is enough to have set IP to dhcp on wan port on wrt1900acs, restart rutx09, immediatelly restart wan interface on wrt1900acs and once rutx09 is up, it will assign private IP to wrt1900acs wan port (modem is not yet connected). I sent troubleshoot file to VidasKac, if you need it, ask me or him to send it to you.