When you Tweet a link, or short link, from one of your communications or promos (events, offers, etc.) to Twitter, your followers are often notified.
Even though the link may contain an image, the notifications your followers see will still look like this if you ONLY Tweet the link:
If you want TO AVOID THIS: ADD TEXT before your link/short link in your Tweets.
That way your followers are notified with your message (so make it something interesting) and when they click to open or see it on your feed/page they will view the full content and image, if one is included.