Basically, TCAS evaluates Range by Range Rate.
In the head-on case, Range 10nm by Range Rate 15nm/min is bad news, in the tailchase case, Range 10nm by Range Rate 1nm/min is nothing to worry about.
There is more to it than that, of course, especially with V7.0, but this should help you to get a handle on it. Think of Tau as a limit value for Range by Range Rate and you're almost there!