Twitter Image Share

You need to use Twitter Card tags in the HTML source of your website. You can use our another plugin https://www.ads-software.com/plugins/heateor-open-graph-meta-tags/ for this.

My pages have those tags already added by Jetpack, but the SuperSocializer doesn’t appear to be finding them.

Twitter card content (image, title, description) will appear with the tweet only after you post the tweet on Twitter, not while sharing on Twitter using our plugin. This is how it works.
Try posting a tweet using our plugin’s share icon and then check your Twitter timeline.

Here’s what I see at each step of the way:

Uploading: https://www.dropbox.com/s/gf0stufec269vpr/Screen%20Shot%202017-10-16%20at%203.20.27%20PM.png?dl=0

Timeline: https://www.dropbox.com/s/21hy2j9qbl4cfbf/Screen%20Shot%202017-10-16%20at%203.21.31%20PM.png?dl=0

It doesn’t appear to be picking up the twitter:image tag (as seen in this source inspection screenshot): https://www.dropbox.com/s/gjurszvqsw59rqq/Screen%20Shot%202017-10-16%20at%203.29.14%20PM.png?dl=0

Your website is blocking the Twitter card crawler from fetching the Twitter card tags.
If you check the url at Twitter card validator https://cards-dev.twitter.com/validator, you will see the message ERROR: Fetching the page failed because it's denied by robots.txt.