(a) RASHI and TOSFOS explain that the Chachmei Yisrael agree with the opinion of Rebbi Yehoshua, who says that the world was created in Nisan. This is evidenced by the fact that they count the Tekufah like Rebbi Yehoshua, and the calculation of the Tekufah affects the times of the Molad and Birkas ha'Chamah (the blessing recited upon seeing the sun when it reaches the same position that it was in when it was created). The only reason why they rule that we count the number of years of the calendar from Tishrei, like Rebbi Eliezer, is because Tishrei is a more important time since it is considered Rosh Hashanah for various matters (Shemitah, Yovel, Orlah, Ma'aser, etc.), as the Gemara (8a) derives from verses.

The RITVA learns like Rashi and Tosfos, that the Chachmei Yisrael agree with the opinion of Rebbi Yehoshua. However, l'Halachah, the Ritva rules that we follow the opinion of Rebbi Eliezer even for calculation of the Tekufah, because Rav (27a) states that the world was created in Tishrei, and Rav has the authority to dispute a Beraisa ("Rav Tana Hu u'Palig"). That is why we say, in the Shemoneh Esreh of Rosh Hashanah, that "this day is the beginning of Creation," following the opinion of Rav (who rules like Rebbi Eliezer) that the world was created in Tishrei.

(b) RABEINU TAM (27a, cited by Tosfos DH k'Man) says that even Rebbi Yehoshua, who says that the world was created in Nisan, agrees that Hashem wanted to create the world in Tishrei. This explains why, even according to Rebbi Yehoshua, we say in the Shemoneh Esreh of Rosh Hashanah that "this day is the beginning of Creation" -- Hashem planned the Creation for Tishrei. That, too, might be why we count the years from Tishrei even though we rule like Rebbi Yehoshua, for that is the time at which Hashem originally planned to create the world.

(Alternatively, Rebbi Eliezer, might agree with Rebbi Yehoshua that the world was planned to be created in Tishrei but was actually created in Nisan. The only argument is whether we consider the Creation, with regard to counting the years, to be at the time that Hashem planned to create the world, or at the time that he actually created it. Accordingly, both Rebbi Eliezer and Rebbi Yehoshua agree that we calculate the Tekufah from Nisan, and the only argument is how to count the years. If so, we effectively rule like Rebbi Eliezer, since we count the years from Tishrei.)

(c) RABEINU CHANANEL is not bothered by the contradiction in the ruling of the Chachmei Yisrael. He says that regarding matters related to the moon, we count from Tishrei, like Rebbi Eliezer, and regarding matters related to the sun, we count from Nisan, like Rebbi Yehoshua. What does Rabeinu Chananel mean? How can we count the Molad of the moon from Tishrei, saying that the moon was created in Tishrei, while at the same time we count the Tekufah from Nisan, saying that the sun was created in Nisan?

Rav David Metzger, in his annotations to the commentary of Rabeinu Chananel, writes that Rabeinu Chananel seems to be of the opinion that the Birkas ha'Chamah is not a blessing recited when the sun returns to the position it was at when created. There is no blessing of that sort.

How does Rabeinu Chananel understand the Gemara in Berachos (59b) which mentions says that the Birkas ha'Chamah is to be recited when the "sun is in its Tekufah" ("Chamah b'Tekufasah")? Rabeinu Chananel there records two opinions of what Birkas ha'Chamah means. The first explanation is like Rashi explains there, that Birkas ha'Chamah is the blessing recited when the sun returns to the position at which it was when it was created, which is actually our Girsa in the Gemara in Berachos. The second opinion is based on the Yerushalmi (Berachos 9:2). The Yerushalmi says that the Birkas ha'Chamah is recited when the sun reappears after not being visible for three consecutive days (due to cloud cover, for example). That is what "Chamah b'Tekufasah" means, and not that the sun is in its original position. According to this second explanation, the calculation of the Tekufah is not related at all to the blessing of Birkas ha'Chamah. According to Rabeinu Chananel, the Beraisa here in Rosh Hashanah which does not consider it contradictory to count Nisan as the first month for Tekufah and Tishrei for the Molad follows the opinion of the Yerushalmi, that there is not Berachah recited when the sun returns to its original spot. (There are those who took Rabeinu Chananel's position about Birkas ha'Chamah into account Halachically. According to the grandson of the Maharal, the Maharal did not recite Birkas ha'Chamah with Hashem's name (Rebbi Akiva Eiger OC 229). Similarly, the Sheyarei Keneses ha'Gedolah (ibid.) writes that they had a Minhag in his community not to recite the Birkas ha'Chamah at all.)

As far as the Molad or Tekufah is concerned, it does not make a difference what is considered to be the beginning of the year. That is, the world was created in Tishrei like Rebbi Eliezer. When the Beraisa says that the Chachmei Yisrael counted the Tekufah of the sun from Nisan, it means that we consider the Tekufah of Nisan to be the first of the four Tekufos of the year. We calculate the Tekufah starting from when Tekufas Nisan would have been in the Nisan before Creation (see Rambam Kidush ha'Chodesh 9:3). As for the Molados, these are calculated from the Tishrei (actually, from Tishrei of the year before the Tishrei of Creation, see TOSFOS 8a DH li'Tekufas).

This approach also answers a question of Tosfos (8b). Tosfos asks how could Rebbi Yehoshua and Rebbi Eliezer argue when the sun and moon were created. It is obvious that they were created in Nisan, because we can examine the astronomical factors and see that if they were created in Tishrei, the sun and moon would be in different places than they are now. How could Rebbi Yehoshua argue about that? The answer is that their argument has absolutely no bearing on the actual time of the Molad or Tekufah.

Why, though, should we calculate the Tekufah from the Nisan before Creation, extrapolating back from Tishrei? Why do we not simply calculate the Tekufah and Molad from Tishrei, when the world was created?

The RAN asks this question (3a of the pages of the Rif). He explains (as does the Mefaresh on the Rambam, Hilchos Kidush ha'Chodesh 9:3) that Nisan is a more preferable time from which to calculate the Tekufah, because it is brighter at that time of year, and all of the produce is beginning to grow.