I've always been wary when using a cash- or points-back site and a voucher code. Sometimes it's worked and I've got both the price reduction and the extra benefit but other times not. I've always been of the opinion that at least I've got something out of it.
Leaving aside whether the wording of the notice from the retailer or site is appropriately accurate I can appreciate that having already incurred a reduction in margin via a discount code the retailer would not also wish to incur further reduction through awarding cashback/Avios

As for making sure the purchase from the retailer tracks reliably it's a good idea to use the private browsing function in the web browser to avoid cookies from previously visited sites preventing purchase tracking.
I often use a completely separate browser than normal, clearing out cookies prior to purchase and disabling pop-up window and advert blocking add-ons.