Its always with the operator (eg orange). But for redemption deals you pay orange the full price each month, and then claim the money back from mobiles.co.uk (or whoever you buy with) every month, quater or 6 months.
You need to check the terms properly because they usually want the original bill, and you have to send the first 3 bills, but then sometimes they tell you, no u send the first 3 at month 4. Then you send it month 4 and they say no it was suposed to be end of month 3 and now its too late lol
Again, not to scare you, it doesnt happen often with good companies, but be safe, read the terms, call a few times to confirm and mark the date in your calender