That's a tough one. If the ballast is not producing any output voltage when turned on it is bad; just hold the tester near each of the wires going to the lamp.
Unfortunately, a ballast may be bad and still show enough output voltage to detect with these testers. And it is easy to hold the tester close enough to the incoming power to pick that up while thinking it is the output from the ballast you are seeing.
So the best method is to ensure there is voltage coming into the ballast (with the tester) then check the outgoing wires from the ballast. If these show power, check the tombstones. If these show power, change the bulbs. If it still doesn't work, replace the ballast. Make sure the tubes are removed when performing these checks, as a tube will light up the tester as well, and from a considerable distance.