I think we had some problem around the time you wrote in with role based reidrects like this - we also saw some odd behavior on an internal site.
Does the “lag” persist even now?
If so, could you send us the x-nf-request-id of such a “deploy completed, but changed rules are not in effect” request? This article explains more about what we’ll need to troubleshoot: [Support Guide] Netlify Support asked for the 'x-nf-request-id' header? What is it and how do I find it?