I haven't written a description yet. Here's a diagram I just made (I'm on my phone rn, please forgive any spelling issues) https://owo.whats-th.is/56opvAS.html
A second try loading each site in new tabs seemed to work, but this time each gave a different ID. One starting 3fa2, the other f918
Reloading each tab then gave two different numbers, 7eb6 and 6f83
Subsequent reloads did not change again.
Loading the sites in to two more tabs, gave yet a different pair of numbers (1934 and 1667), reloads of those tabs yeilded another pair (b308 and 3df8)
It works on Fennec, even in private mode. (Fennec is the F-Droid Firefox build.) Do you have any addons? It works with uBlock Origin on desktop, haven't tried mobile.
I'm on a desktop using FF with uBO, both with fairly locked-down configs, and it doesn't work for me. That is, both websites eventually lead to a broken page because of too many redirects, and the URLs in the URL bars of each tab do not contain the same ID.
Without digging too deep into what your websites are doing, I did notice that they're trying to set / read cookies, which is a) being blocked by uMatrix in general, and b) perhaps being blocked by me having configured FF to block third-party cookies in particular.