In Tehillim 114:2 [MT], we are told after the Exodus that: "Yehudah became His Sanctuary, Yisrael His dominion (הָֽיְתָ֣ה יְהוּדָ֣ה לְקָדְשׁ֑וֹ יִ֜שְׂרָאֵ֗ל מַמְשְׁלוֹתָֽיו)".
The interlinear Schottenstein Edition of [Psalms] by ArtScroll shows a Commentary - related to the statement " Yehudah became His Sanctuary " (הָֽיְתָ֣ה יְהוּדָ֣ה לְקָדְשׁ֑וֹ) in [Tehillim 114] verse 2, stating :
God singled out the tribe of Judah to be the family of royalty, because they sanctified God's Name at the Sea of Reeds. Led by their prince, Nachshon ben-Aminadav (נַחְשׁ֖וֹן בֶּן־עַמִּֽינָדָֽב), this tribe was the first to jump into the threatening waters.
In the desert [Bamidbar 1:7], Nachshon ben-Aminadav (נַחְשׁ֖וֹן בֶּן־עַמִּֽינָדָֽב) is mentioned as the Prince of Yehudah. - Yet the Torah does not mention Nachshon's jump into the Reed Sea.
How did Nachshon ben-Aminadav (נַחְשׁ֖וֹן בֶּן־עַמִּֽינָדָֽב) originally get linked to Tehillim 114:2?