Using Mockito to verify that an object is saved
Looking at your production code, my positive test case would check the getToken() and savePayload() methods were invoked; and the same string returned from getToken() was also returned by processTokenRequest().

Some points:


I wouldn't use the any matcher with verify(). Explicitly state what you want. 
No need to return value from a method when you don't use the returned value i.e. doAnswer for savePayload() is unnecessary.
As mentioned, times(1) is the default for verify() and used in your first test.
Tests shouldn't throw exceptions.
Static imports often make short code easy to read.
Is isNotBlank() enough?