When by the laws of any other state a premium or income or other taxes, or fees, fines, penalties, licenses, deposit requirements or other obligations, prohibitions or restrictions are imposed upon Iowa insurance companies actually doing business in the other state, or upon the agents of the Iowa companies, which in the aggregate are in excess of the aggregate of the taxes, fees, fines, penalties, licenses, deposit requirements or other obligations, prohibitions or restrictions directly imposed upon insurance companies of the other state under the statutes of this state, the same obligations, prohibitions or restrictions of whatever kind are in the same manner and for the same purpose imposed upon insurance companies of the other state doing business in Iowa. Insurance premium taxes paid which were not paid under protest shall not be refunded if the refund claim is based upon an alleged error or mistake of law or erroneous interpretation of statute regarding the validity or legality of this section under the laws or constitutions of the United States or this state. For the purpose of this section, an alien insurer is deemed domiciled in a state designated by it wherein it has established its principal office or agency in the United States, or maintains the largest amount of its assets held in trust or on deposit for the security of its policyholders or policyholders and creditors in the United States, or in which it was admitted to do business in the United States. This section does not apply to ad valorem taxes on real or personal property or to personal income taxes.