How content is displayed on the social media networks is largely determined by the networks themselves. We conform to their requirements, and they decide how to handle links and images as they are posted. Usually, this means that the social media network will crawl the link, pull in an image from that link, and show the viewer where that link will take them. Generally speaking, this is the default behavior, but they all handle it in slightly different ways.
For Facebook, we do have an internal-only setting that allows you to override this behavior, so you can use the image, title, and description from the post in your platform. However, when you use this setting, Facebook will show the "original" source of the content, which means the URL of your Dynamic Signal platform will be shown. So it's a tradeoff ... if you want more control over the image and content, Facebook will reflect that your platform created it. If you allow Facebook to use a preview of the final link instead, you can keep your platform private, but you can no longer customize the images.
On LinkedIn, the situation is similar, but two key differences. LinkedIn starts off by showing your platform URL as the source of the content. We have an internal-only setting that will override that behavior, having LinkedIn show the URL of the content instead of your platform. As a side effect, however, they will also not share click data coming from their mobile apps. (Because you're losing that trackability, most customers will not use this option. Using our Third-Party Tracking feature can mitigate this for content coming back to sites you own.)
Twitter works similarly to Facebook. By default, they will crawl your link and display that URL, along with an image from the link, in a Twitter Post Card. Again, we have an internal-only setting to allow you to force Twitter to use an image from your platform instead. However, Twitter will not display this as a "card" when this setting is used ... it will just be a link to the post and the image embedded.
There is no best setting for any of these networks. It all comes down to what you're trying to accomplish, and how important it is to you to keep the URL of your platform private. Remember, each of these networks is doing this to improve the trustworthiness of content found in their networks ... either they will show you exactly what the content is and where they will be taken when they click, or they will show where the content actually came from.
We tend to recommend that social media managers accept that they can't really control the output on the networks and be seen as trustworthy. This will mean that occasionally a post will show up without an image (if the URL of the post doesn't have it's images properly meta-tagged), the preview text may be less than ideal, or a variety of other tradeoffs. Anecdotally, we're seeing that the more our customers try to force images and override these settings, the fewer clicks they get, because there's the subtle connotation that the content should not be trusted. (The public has quickly adapted to the way these networks display trusted content.)
If you want to change any of these internal settings, your Customer Success Manager can take you through the options and set them for you, or if you know exactly how you want them set, our Support team can do it as well.