Ptolemy I Soter (c. 367-282 BCE) received the epithet from the Rhodians after he relieved Demetrius's siege of Rhodes in 304 BCE. Antiochus I earned Soter for defeating the Gauls, the elephant victory, c. 275 BCE. Demetrius Soter of Bactria and others followed; the epithet migrated from vote of gratitude to dynastic furniture.
The trajectory every honor follows: voted once for a real deliverance, copied onto every successor's coins, until savior meant little more than incumbent. Numismatists read the decay in the dies.
The context that matters for the New Testament: first-century ears already knew soter as the emperor's and kings' title, Caesar as savior of the world on inscriptions. Calling a crucified Judean soter was not devotional softness; it was a direct counterclaim in a crowded title market, treason in a single noun.
If the title is earned by rescue, what does it mean when the grandson inherits it?