Why, in the case of Shimon Hatzadik, does the Gemara say that they
noted the time and found it to be correct, whereas in the previous case they did not?
Good question. Actually, it seems that what you are asking is what they refer to in Yeshivah as "a kasha oif a mayseh." The reason the Gemara said it only in the case of Shimon ha'Tzadik is because they didn't do it in the story of Yochanan Kohen Gadol.
It is possible that they checked in Shimon ha'Tzadik's case because it was an event with a definite time -- the death of Gaskalgas. In contrast, the victory in the battle of the Pirchei Kehunah was prolonged.
The Yerushalmi only mentions that they synchronized the times in the case of Yochanan Kohen Gadol and the Pirchei Kehunah, and not in the case of Shimon ha'Tzadik. The Yerushalmi, though, mentions the Yochanan Kohen Gadol story last, and not first.
To coordinate the versions of the Bavli and Yerushalmi, it is possible to suggest that the statement "they checked the times..." refers to both of the stories, and that is why the Beraisa wrote it after both of the stories, both in the Yerushalmi and the Bavli.