Customer Specific Pricing does not integrate well with other apps that display products outside the store. This is because liquid code is added to your theme files to hide the customer specific pricing until the customer is logged in.
When products are displayed outside the store, the third-party apps retrieve the range of the lowest and highest priced variants from your store. Some of the common apps used include Pinterest, Facebook, and other product feeds.
As these apps do not use the liquid code installed in your theme, there is no solution to this. Unfortunately, we have no control over how these apps pull their data.