Site detection is done from the CMSSiteFilter in your storefront extension. The default behaviour is to use the site from the session and only look up the site when it isn't available from the session or clear=true is in the query string.
You can change this behaviour so that it looks up the correct site on every request and I have done this before when doing the same thing as you where different sites share a single domain (and therefore share session cookies)
If you do this then you probably want to override the default ContextInformationLoader so that you only initialise the site if it has changed from the current session value.
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