Google's John Mueller said that while Google will process your disavow link file immediately, it will take some time for Google to disavow the links within it. John said on Twitter "The files are processed immediately. The links are disavowed over time - there is no fixed timeline."
Here are the tweets with context:
The files are processed immediately. The links are disavowed over time - there is no fixed timeline.
— 🍌 John 🍌 (@JohnMu) June 1, 2019
I assume the process overall is pretty quick but don't expect the disavow process to happen within a couple of hours. It probably takes a few days or weeks to fully have Google update to realize those changes.
Forum discussion at Twitter.
