Some countries have this tax your mentioning, however, there is a easy way to avoid it just a formality. Also the question "What tax does a offshore company pay?" is too board, I mean what offshore country do we speak?
IBCs in Belize and Seychelles pay zero tax. If I recall correctly, it's technically an exemption that lasts 10 or 20 years from incorporation but is automatically extended after that period.
Sorry for joining the thread. I understand that they never have to pay tax at all because they had status to be foreign and not doing business national?
That varies between jurisdictions, but is generally true. As long as you do not deal with the local market in offshore jurisdictions, no tax is levied.