Well, if you have a IBC company in Cyprus the company will not have to pay any TAX, however if you take some money out of the company and transfer it as for instant payroll you as a person will be subject to TAX in your home country / country of residence. There are ways around this but I won't go and publish it here.
The income can stay with the offshore company
and you won't pay any TAX if the authorities in your country of residence don't know that you have a offshore company
, if they know it will be different but it again depends on which country you are a resident of. For instant in many European countries the TAX authorties would not accept that you keep the money in the offshore company without paying tax if your only income source is this company!
Again there are workarounds on this and some loopholes but you should speak with one of the professionals to get the answer on this.
I can just speak for ourselve which we created a great setup for our purpose.