Maybe it has to do with the fact that Magus can increase his Mag Def. Perhaps this magical ability is really what the Masamune is absorbing...It seems as though the Masamune, and likewise with all Dreamstone, absorbs focused (Lavos) energy. As is the case with the Mammon Machine and Magus because for one, he's summoning Lavos, and two, he has the ability to increase his magical defense (via magic). Also, can we really say for a fact that Magus doesn't have his magical ability from Lavos? He obviously knows of it's existence, and it's power, and he was even attempting to summon it. So why couldn't he have gained magic from it?
Also, in Zeal's transformed state, she is more directly drawing Lavos's energy, so perhaps that plays a part in it.
And really, we don't know about Cyrus. Perhaps he does have a personal agenda against Magus...Cyrus really was a quite undeveloped character in the game. He seemed to have a true love of the throne, like Frog would later have.