When I try to connect to Alfresco over HTTPS I can get CMIS seesion object and other repository information. But all subsequent calls to repository does not reach Alfresco load balancer and instead I see requests made to local tomcat instance.
Please check if you have configured your system correctly to enable SSL use via a loadbalancer, like one would do in production. It does not sound like you have... Specifically I believe you are missing configuration in alfresco-global.properties necessary for Alfresco to generate the proper response URLs in the initial session establishment, so that the CMIS clients knows which HTTS URLs to call.