Good on the Italians. Mind you, somewhat ironic given the country's reputation for having a corrupt civil service.
According to my country's tax authorities, the dual-taxation agreement between European States merely gives tax payers living in one State but being paid in another, a right to receive credit against their tax liabilities in the state of residence.
In other words, if Italian tax rates are 10% higher than those in Ireland, and you live 183 days or more of the year in Italy, the Italian government are perfectly entitled to seek the 10% difference from you.