I tried to log-in to your site to check the settings for your custom archive, but the credentials you provided don't work.
I checked on a local test site, where things appeared to work normally, so that it looks to be something particular to your site.
Can you review the settings for the custom author archive at Toolset > WordPress Archives, in particular those shown in the screenshot about which post types ought to be displayed?
If those appear correct (to only show the custom post type in question) then perhaps you could provide working credentials so that we can check your site?
(Note: in your question you said the archive should show CPTs. If it is actually set to show standard Posts, try changing the setting to something else, and then change the setting back to Posts, in which case I suspect it will fix the issue.)