Your example using ii-V-I for instance, if the progression were in C Major would be as follows. Dm7-G7-Cmaj7. If we took the V7 and reviewed the notes in the chord, it would be; G-B-D-F....To substitute the tritone, we would need to move three whole steps in the direction that will match to substitute with it. From G7 the three whole steps give the Db7.
Db7 = Db-F-Ab-B. Now both chords share the same tritone (F-B), only inverted. The 3rd and b7 switched.
Now the progression is; Dm7-Db7-Cmaj7....and creates a downward movement with the Root notes. It also reinforces the 3rd and b7th of the chords downward as well (Dm7= F-C....Db7= F-B........Cmaj7= E-B).
Sorry I don't understand the other portion completely. You mention that F# is the IV of C#. Just in case it may help, C# is also the V of F#.
