We need to document default behaviour of publish action in combination with p13n and also how to adjust it.

Publish (without subnodes) action by default doesn't publish the page variants. This can be simple adjust by modifying default-personalizationActivation command. See https://jira.magnolia-cms.com/browse/PUBLISHING-87?focusedCommentId=249484&page=com.atlassian.jira.plugin.system.issuetabpanels%3Acomment-tabpanel#comment-249484

However component variants are publish by default with the page publication. This is because the component variants are not so visible (they are not visible in page browser only in page detail). Again this default behaviour can be adjust by configuration of the commands.