For another example of timelines I will add my experience so far.
I submitted mine 8/31. DH did his 9/1. DH's was processed on Sept 6th and we received it on Sept 13th, for 12 days total. Awesome!
My payment was processed 9/3 and as of 9/21 it's still showing "In Process". 3 weeks and not even done/mailed yet. I'm not sure why there is such a discrepancy, especially when they say they process them in order, but they do say it takes 6-8 weeks so I will have to wait some more. Our next cruise check in is in about a month so I hope to have it in time for that.