how long does it take for disavow tool to work?

There is no fixed timeframe on this. Google have gotten a lot faster over the years at dealing with things like this. They can crawl and index pages almost instantly. At the end of the day though, the ranking factors are still a mystery to us. Maybe they read the disvow urls instantly and there are other factors impacting the result not indexing. 

Generally speaking, most people tend to wait a few weeks for any changes to show up in the SERP results. Nothing changes quickly there and even when they do, they are often subject to regular fluctuations for a short period of time while things settle down.