In one of his talks, the Lubavitcher Rebbe zt"l explains:
The Splitting of the Sea was the first intimation that the physical and the spiritual could combine (which ultimately became a reality a few weeks later, at the Giving of the Torah), since "the sea" represents the spiritual worlds that are hidden from our ken (like the depths of the ocean), while "dry land" symbolizes the material world that is revealed to our gaze.
On the other hand, Amalek's attack on the Jewish People demonstrated that this unity between the two realms is far from complete.
So Yisro, realizing this, understood that it would be up to him to come join the Jewish People in making this a reality. He was uniquely qualified to do so, as his era's prime expert on all idolatrous deities (i.e., manifestations of materiality), who would now come and acknowledge that G-d creates and maintains all of existence.
I've also heard another explanation whose source I don't now recall (it's sort of similar to a comment in footnote 33 there, but taking a somewhat different tack):
After the crossing of the Yam Suf, all of the nations of the world were deeply impressed by the display of G-d's power, and were afraid to attack His people. Until Amalek came and recklessly "jumped into the boiling tub," thereby making others less nervous about doing the same (Rashi to Deut. 25:18).
Well, then, this set Yisro to thinking. If even after such an awesome demonstration as the Splitting of the Sea it's still possible for there to be an Amalek who ignores the whole thing - why, then, this shows that one can't just be impressed by it and remain as he was; sooner or later this excitement will evaporate, cool off, and then one may descend to the level of an Amalek. He has to act, now, while the impression is still fresh! And that's what he did.