Impossible to see some guest data with a logued user (aka my home page)

I have a demo web site with three languages. All the three lang were validated for the home page. The home page is visible by guest user (cf screenshot 1).

I created a "steven" user and gave him some rights only on a level 2 page (+ a role to enter into the admin center else he can not login the site any more).

Trhough the /administration url I login with my steven user. Then I exit the administration. Impossible to access to the home page. I can access to my second page (and the page path does not display the home page) and I flushed the cache. Same behaviour.

It looks like the content available for the guest user (not group) is not also automatically visible for all other logued users which should be the case.