Rashi finds it necessary to point out, on the Gemara's quotation (99a)from Zecharia, both that it's in Terei Asar and that this Zecharia is not the same as the one from Bayis Rishon. Why does Rashi find it necessary to point this out?
The Gemara is making a point of the fact that Zecharyah predicted the coming of Moshi'ach despite the fact that he lived after Chizkiyah (proving that even after Chizkiyah Hash-m still plans to send a Moshi'ach). This is only understandable if the Zecharyah it mentions lived during the epoch of the second temple, as the Gemara says.
Perhaps Rashi felt the reader would easily be confused by the fact that the Gemara just three Dafim back mentioned the blood of the slain *prophet Zecharyah* ben Yehoyada which was found by Nevuzaraden when he destroyed the *first* Mikdash. That is why Rashi emphasizes that the Zecharyah of our Sugya is from Trei Asar.
In addition, the Gemara at the end of Makos cites a verse that seems to associate the Zecharyah of Trei Asar with Uri'ah, who prophesied during the times of the first Mikdash. That is why Rashi emphasizes that our Zecharyah lived during the times of the *Second Temple* -- as the Gemara indeed concludes in the Sugya at the end of Makos.
I would like to add a time frame to some of the events discussed.
According to the Midrash Rabah Koheles 3:1:16, Zecharyah ben Yehoyada was killed 252 years before the destruction of the first Temple. (The Chidushei HaRedal ad loc. emends the text to read 238 years instead of 252.) The Churban of the first Beit HaMikdash is generally accepted to have occurred in the year 3338.
On the other hand, Chizkiyah's reign is generally accepted to have taken place between the years 3199 - 3228.