Problem with cache using both http and https

Hi !

I tried to move a full website today to a new server supporting both HTTP and HTTPS for the same domain.
My problem is :
- I regenerate the website clearing the current cache.
- Someone goes to the website using https://www.mydomain.tld and see that all the links are prefixed by ’https://’ that is correct.
- But when another people (or the same) goes to the webstite using http://www.mydomain.tld, all the links are still prefixed by ’https’ because of the full url caching

I haven’t seen any option in moderator web interface nor in includes files.

What is the best way to avoid this problem without disabling manually the caching for each document ? Is it possible to tell modx that all cached URL must be relative to / instead of http(s)://www.mydomain.tld/ ?

Thanks for your answers,

Regards.