Do you have some cache activated ?
do you have the error when you are login ?

I don't see how the result can be different between 2 consecutive requests

Don't use the progressive one, not a good one the conversative is the one to use
Progressive is a different cache per user (no interest)

stackoverflow.com/questions/12739297/wha...ive-caching-in-jooml

Conservative caching is the standard type of caching. Here’s how it works:

A visitor visits a page on your website.
Joomla checks if there is a non-expired version of that page in its cache directory.
If the cached page exists (and it’s not expired), then Joomla will serve it to the visitor – otherwise, a cached version of the page is created, and that cached version will be served to the visitor, and to every other consequent visitor, as long as it’s (by “it” we mean the page) not expired.
The above scenario is typical and is how most developers implement caching.

Progressive caching works the following way:

A visitor visits a page on your website.
Joomla checks if a cached version of that page exists for that visitor and it’s not yet expired.
If that cached page exists, then it’ll be served to the visitor, otherwise, Joomla will create the cached page for that specific visitor and then will serve it to him.
If another visitor (who has never been on that page) visits that page, then Joomla will not serve the cached page of the previous visitor, instead, it will create a cached version of that page
specifically for that user, and then serves it to him.