As of revision 2040, CEF now adds support for complete isolation of storage and permissions (cache, cookies, localStorage, access grants, etc) on a request context basis. This is also now in CEFSharp.
To make sure that no sessions overlap between multiple instances, simply create a new RequestContextSettings object, set PersistSessionCookies and/or PersistUserPreferences to false, and assign it to your browser while creating a new RequestContext - I am not sure if setting them to false is completely necessary for multiple instances, maybe someone else can give some info on that.
//usually ChromiumWebBrowser setup goes above this
RequestContextSettings requestContextSettings = new RequestContextSettings();
requestContextSettings.PersistSessionCookies = false;
requestContextSettings.PersistUserPreferences = false;
webBrowser.RequestContext = new RequestContext(requestContextSettings);
This had been giving me headaches for a while and this appears to finally solve that issue.