Thank you for your question. The short answer would be, no, there is not an explicit list of apps that are supported by OMC. Having said that, the OMC does have SSO capability for any native mobile apps that support SAML.
Without having more context, it will be difficult to fully assess the reason you're experiencing those issues, because each organization's setup has subtle differences. I would recommend opening a ticket/case with Okta support, so we can take a look at your org configuration and help you get everything set up and working to its full potential. You can open a case by navigating to: https://support.okta.com and clicking "Open a Case"
In the meantime, if you'd like more information on OMC, here are some helpful resources to get you started: https://help.okta.com/en/prev/Content/Topics/Mobile/Okta_Mobile_Connect.htm http://developer.okta.com/use_cases/mobile/okta_mobile_connect
Thanks again for contacting us. We look forward to helping you. Justin M. Bergez