I will see if I can find it. Pretty sure the LATEST time I saw it was a John Mueller webmaster central video on you tube. I will try to find the exact part.
Unfortunately, they made it harder to search on the google webmaster tools help forum via an author's name. I will see if I can find the posts about that as well.
When you submit the disavow file, google has to go and recrawl the links, then compare them to your disavow file, then calculate the new page rank (and other factors). This "takes some time" according to John Mueller:
Starting around 12:20 he starts to talk about some of the things that have to happen for the disavow tool to take effect.
but I will look for the comments regarding the months time frame.