Dear bp27,
Thanks for asking. Indeed, your understanding is the prevalent one, however, it seems to be incorrect.
Sources:
1.Sefer Hayashar, siman 221
2. Book by Rav Zinni of Haifa, Shitat Rabbeinu Tam b”ven Hasmashot
3. Hama’ayan, Vol. 200, presentation by Rav Yaakov Levinger
A synopsis: According to all, tzet hakochavim follows ben hashmashot, and is defined by three medium-sized stars.
The issue is to resolve the two lengths of bein hashmashot, one 3/4 mil, the other 4 mil. Rabbeinu Tam resolves this contradiction by postulating a thick window or tunnel which the sun goes through. The first window is when the light of the day starts dimming (way before sunset).The second is when the sun exits the end of the window or passageway. This is tzet hacochavim, no light is left. What we call sunset is somwhere in between, but neither the entrance into the tunnel, nor the exit from it.
The upshot is essentially twofold:
1. All times are counted backwards from when the stars appear, which is the ony universally agreed upon ( agreed upon by all the sugyot in the gemara) event.
2. What counts is not the position of the sun, but rather the amount of light still experienced on Earth. This amount of light is influenced by the setting of the sun, but there is a diminishing of light even before sunset, and still a considerable amount of light after the sun sets. It is this gradual change of lighting that Rabeinu Tam considers.
I know this is different than what is practiced and taught. Please read at least the Sefer Hayashar and one of the other sources (they both quote the sefer hayashar anyway). It will explain everything, including those Rishonim who understood Rabeinu Tam correctly, and those Achronim who did not.