I am assuming the the browser is the one caching the page. If this is the case, you can't simply remove the cache from the browser when they log off.
Instead, you will need to tell the browser to not cache any of the pages.
You can do this with a simple action filter and override the OnResultExecuting
method
public override void OnResultExecuting(ResultExecutingContext filterContext)
{
filterContext.HttpContext.Response.Cache.SetExpires(DateTime.UtcNow.AddDays(-1));
filterContext.HttpContext.Response.Cache.SetValidUntilExpires(false);
filterContext.HttpContext.Response.Cache.SetRevalidation(HttpCacheRevalidation.AllCaches);
filterContext.HttpContext.Response.Cache.SetCacheability(HttpCacheability.NoCache);
base.OnResultExecuting(filterContext);
}