If the tool is indeed the right thread for BB tapping, then you can't do it 'too much'. It will clean and chase the thread until it is the right size.
What you may have done in the initial installation is remove a little of the material of the BB thread, making it very easy to thread on now. As there is perhaps less friction b/w frame and cups than is normal, I would use some light thread lock to make sure they don't back out in use. As you said yourself, once tightened to spec they are OK, and that is the only way they should run anyhow.
If in doubt, try another BB to see if it is indeed the frame which is at 'fault', a good bike shop should also be able to help.
What you may have done in the initial installation is remove a little of the material of the BB thread, making it very easy to thread on now. As there is perhaps less friction b/w frame and cups than is normal, I would use some light thread lock to make sure they don't back out in use. As you said yourself, once tightened to spec they are OK, and that is the only way they should run anyhow.
If in doubt, try another BB to see if it is indeed the frame which is at 'fault', a good bike shop should also be able to help.
