I don't think they've explained it well – of course you should push them on this.
Basically it is becoming quite standard practice that merchants do not award any commission to any referrer for shoppers that use voucher codes. It makes sense, it stops double-dipping.
If you've used vouchers in the past, that's why they haven't been appearing because Tesco Wines hasn't authorised them at its end.
Look at how Quidco handles it, it's quite plain: "Cashback only eligible on Quidco advertised vouchers"