Won my appeal - how long to wait for backdated payments?

Having been on Invalidity Benefit/Incapacity Benefit/ESA since 1990 due to severe mobility problems I got 0 points in my September 2016 assessment. Mandatory reconsideration was also denied (if these were independent people rather than another member of the DWP who in most circumstances will back up their colleague then millions would be saved in not having to go to tribunals if the decision was overturned). Judges get £300 as do doctors but forgotten if that is per day or per tribunal.
I had my ESA stopped in September 2016 and was unaware that you could apply to keep it until tribunal which I read recently but the DWP won't broadcast that I'm sure.
I went to my tribunal on December 10 with only the judge and doctor there (no DWP representative). The judge asked me two questions and so did the doctor. The judge asked if I had anything more to say and I said everything that I had to say I had sent in by email to the tribunal and they had seen it. After five minutes that was it! I was told there and then that my appeal had been successful. I had to wait outside for a while until everything was typed up instead of the secretary the judge himself came out and handed me the notification and said I had been awarded two lots of 15 points and he didn't know why I was there?
I was lost for words however  but I should have said you should address that remark to the DWP!!
The whole system is a shambles and I was upset and angry that a whole year's worry had been eliminated in just five minutes in the tribunal.
Anyway my question is how long should you have to wait for the DWP to contact you regarding back payments and future payments? It's been 19 days now and thought they would have been in touch before now.