Hi,
The auction itself is handled correctly. At its end date, HikaAuction closes it and marks the product as sold, without waiting for the payment of the winner. That is why the product page displays the auction as finished and why the buyer finds it in his won auctions.
What you see on the seller side comes from the listing itself. That page is the products listing of the vendor panel, and it displays all the products of the vendor, whatever their auction state. It has no auction filter, and a sold auction product is still a product of the vendor, so it stays in the list next to the ones still running. It is not a status which fails to be updated, it is a filter which does not exist yet on that listing.
We are going to add an auction filter to that products listing of the vendor panel, so that a seller can display only his running auctions, only the finished ones, or all of them with the. next version of HikaAuction.
In the meantime, one thing not to do : do not unpublish the finished products to clean up that list. The won auctions page of the buyer only displays published products, so the winner would lose the access to his auction and to its payment.
And if what you need in the meantime is a public page with the auctions currently running, you can create a product listing menu item and set, in its options, "Show auctions" to "Only auctions", "Auction start state" to "Only started auctions" and "Show expired products" to "Only valid products with expiration". Those three options are added by HikaAuction to the product listing menu items and modules, and that combination gives the auctions which are running at the moment, but for all the vendors, not just the current one.