For onshore company, you would be required to pay VAT for the country where you company has been incorporated only.
For offshore, you would be required to pay VAT to the country where you are citizen. But this is only if you declare your company with the local tax authority (Which I don't think you should do if its an offshore). However, you need to be very cautious and with FATCA coming up (If your are US Citizen), IRS will know that you hold an offshore bank account.