If you don't have an Multi Spark Discharge box (MSD 6AL, Crane Hi-6S, ect) you don't need the adapter.
You only have an aftermarket coil, so it should be wired up the same as OEM and your tach should work properly. Somewhere along the line, your tach is not getting any type of signal from the coil. You need to go thru your wiring and figure out what isn't hooked up properly.
You don't need to go out and buy an MSD box to make it work. You could, but unless you are building a racing motor you don't need it and it would just be a waste of money.