I’m sorry but I am not familiar with Invision’s solution, so this is tricky.
I’m not sure why you would ever need to share API keys with a third party CMS. You should (!) be able to integrate Tweets and timelines from publish.twitter.com if you need to include Tweets on your site.
Cards are enabled by HTML markup on your individual pages. In theory if you have access to the page header you can add the markup yourself. I don’t know the Invision system so I don’t know what access to meta tags it provides.