Congratulations on winning your case! Unfortunately, much depends on the office processing your payments, but you should see payments within the next couple of months.
I'm assuming you were not represented by an attorney (or non-attorney rep). If you were, you should contact him or her to discuss this.
Make sure you understand the basis for any reductions to the maximum eligibility amount. You should receive a letter explaining the reductions in detail. If you do not understand any reductions that are made, call the number on the letter and politely request an explanation. If you are not satisfied with the explanation or have any question about whether you are receiving what you are entitled to, consult a local attorney. If there are reductions, and an attorney believes they are illegitimate, he or she can help you fight for the additional money.
While it can vary, usually within 30 days you should know when your payments will start and how much back pay you will get.
Actual legal advice can only be provided by an attorney licensed in your jurisdiction, with experience in the area of law regarding your question. The information provided is for informational purposes only and is not legal advice.
SSI may take longer than (Social Security disability) because unlike Social Security disability, the payments are based on somewhat complicated factors having to do with your assets and income including income that is deemed, that is assigned to you as if you have it, as result of certain types of help you have received from others. You know now that you qualify for the benefits but it could be a couple of months until it is computed how much an SSI check would be.
Disclaimer: the above does not constitute legal advice and is only an opinion of the author as to current law. You should consult an attorney with questions about your particular situation.