I get this problem regularly. I am using 8 cell silicone moulds. I have 9 varieties of soap. 4 varieties get the soda ash on the parts inside the mould, usually on the corners. However this isn't a superficial issue, it goes right into the soap a couple of millimetres. It looks like the corners have bleached and sometimes the corners and bottom edges are crumbly, but not always. In this case steaming or wiping does not work. I had one bar which I used and after over a week of regular use you could still detect where the corners were lighter in colour to the rest of the soap. I do sometimes get more "normal" soda ash on top too. I don't know why it happens, and to only some of my soaps, all of which have a similar base recipe. My last batch I took Penelope Jane's advice (or a variation thereof) and CPOPed the worst affected bars to force gel as well as covering them with greaseproof paper and a towel to try and exclude at least some of the air (cling film refused to cling to the silicone moulds.) I also left them in the mould for at least two or three days before unmoulding. In three of the four varieties it worked. The worst affected one, (ironically everybody's favourite soap, lemongrass and poppy seed) still got the faded corners and edges though no crumbling this time. It is very frustrating and I still don't now why it happens and why only some soaps. There doesn't appear to be any logic to which ones it happens to and which it doesn't. I did wonder whether older silicon moulds were the problem but I'm not sure. Forcing gel certainly did help in most of the cases, so it might be worth a try. Some people spray alcohol on top as well, though this won't affect the ash inside the moulds. I did wonder whether oiling the inside of the moulds with mineral oil might work, though I haven't tried this myself. I think some people do this to aid unmoulding?
Good luck and please post if you are successful in curing the problem. I for one would be very grateful.