The problem is
listModel.addElement(listaRosa.getSelectedValue());
listModel.removeElement(listaRosa.getSelectedValue());
you may be adding an element and immediatly removing it since both add and remove operations are on the same listModel.
Try
private void aggiungiTitolareButtonActionPerformed(java.awt.event.ActionEvent evt) {
DefaultListModel lm2 = (DefaultListModel) listaTitolari.getModel();
DefaultListModel lm1 = (DefaultListModel) listaRosa.getModel();
if(lm2 == null)
{
lm2 = new DefaultListModel();
listaTitolari.setModel(lm2);
}
lm2.addElement(listaTitolari.getSelectedValue());
lm1.removeElement(listaTitolari.getSelectedValue());
}