In a previous post the point was raised that there is a petur of תשבו כעין תדורו on the first night. I believe that this is very much debatable.
There is a machlokes rishonim what the hekesh means. The 2 possibilities are:
1. It is an extension of the regular din of yeshiva b'succa. On the other days of Succos ratzah ochel ratzah lo ochel, on the first night the hekesh says that you must eat. However, the regular din of teishvu k'eyn taduru applies.
2. The hekesh creates a new chiyuv of achila on the first night unrelated to the regular din of yeshiva b'succa.
There are a number of nafka minas
1. What if rains the first night? Do you need to eat in the succah? This is a machlokes harishhonim. According to 1, you would not. The regular din of teishvu k'eyn taduru applies. According to 2 you would need to eat as there is a chiyuv achila.
2. What is the shiur, k'beitza or k'zayis? According to 1 the shiur would probably be k'beitzah like all of Succos, according to 2 it is a din of achila and the shiur of achila is k'zayis (again a machlokes rishonim).
In any case, according to everyone teishvu k'eyn taduru would certainly apply on the first night to sleeping in the succah, the only time it may not apply is to the first k'zayis that you eat.
The hekesh to Pesach is to be mechayev him to eat a kzayis (or k'beitzah) in the succah after that everyone agrees teishvu k'eyn taduru applies.