Tyrian shekalim were first minted apparently in ca. 127 BCE, shortly after
Hyrcanus I
gained power in ca. 132 BCE. It is unclear when Tyrian coins began to be used commonly as the
Temple Tax, but it was likely during the
Hasmonean period, perhaps under
Hyrcanus I. Keep in mind that it does not appear that Tyrian coins were required by fiat.
See for example Schafer, The
History of the Jews in
Antiquity (
preview) or Regev, The
Hasmoneans: Ideology, Archaeology, Identity (
preview).