I used avios estore a lot and lately BA more as the former is shutting. I've had tens of thousands of points back with at least 90% I think with no issue. I do operate on the basis of these and cashback sites that they are not guaranteed though, so I don't get any stress if something doesn't track, which inevitably will happen from time to time.
Things that I have found to make things track better:
- do not have any windows of the retailer open before you click the link from the ba/avios store. You can browse on the retailers beforehand and add things to basket etc, but make sure to close all instances of the retailer's windows before you click the ba/avios link.
- once you've clicked on the link and the retailer window comes up, do not close the window. Try not to open additional windows or tabs. Ideally checkout as quickly as possible. Maybe do all the browsing and adding to basket before you click the link per the first step above.
- if you've bought something and need to buy more from the same retailer again, make sure to close all instances of the retailer again and follow top two steps above.