At the moment StoreFeeder does not typically contact channels regarding order refunds.
If you do a refund on the channel you will also need to replicate that in StoreFeeder to mark the order as refunded and return the stock if necessary. (Except for eBay where we delete the orders in StoreFeeder once canceled on the channel as eBay can re-use order numbers).
There is a guide on returning orders within StoreFeeder here: Returning Orders.
We also do not push refunds or returns to channels at this time unless you are opted in to our eBay refund feature or are beta-testing the amazon refund feature.
If you are interested in using our eBay refund feature you can contact the support team to have it enabled but you may want to view our knowledgebase here first: eBay Refunds