Since customer specific pricing can be based on complex/custom pricing logic outside of standard Magento practices, you have to enable "Serverside" mode to show these to customers in recommenders as these will not be sent in the feeds.
"Serverside" mode means all recommender display is routed via Magento to ensure correct pricing and products are shown to the correct customers.
We also support customer group pricing in Product feeds, see the “Data Feeds & Indexing” section for more information.