Having 2 website on the same server using ember-simple-auth logs both out

I currently have 2 of the same site (one for production and the other is a development version) on one server and I have an issue with the ember-simple-auth for both of the site. Whenever I log in on one of the site, it works perfectly fine, the session works and everything works as expected. However, when I have both of the site open on different tabs (on the same browser and same window) and I try logging on one of them, they both log out creating an error in the console saying:

"The authenticator "authenticator:oauth2" rejected to restore the session - invalidating…"

On the other hand, when I have one of the site open on a regular browser and the other one on the same browser but in incognito (no caches), they both work perfectly fine (e.g. none of them logs out and everything works as expectedly). It works perfectly fine too if I open one site in one browser (such as Chrome) and the other site in a different browser (such as Safari).

My first guess is that these 2 different site has the same session used in cache but I could be wrong. If you have any idea on why this occur or you have a solution, please let me know.