הרב איתן שנדורפי suggests that it is to give praise to those Shevatim, that despite all being born in Padan Aram, they were still tzadikim, based on Rashi Bereishis 25:20. He shows that this is a commonly added piece of information all over Bereishis.
Gershon Gold pointed out the following answer from the Nesiv Hayashar here, that based on the Alshich's understanding that Lavan's switching of Rachel and Leah was the cause of going down to Mitzrayim (because otherwise Yosef would have been born first and not gotten into fights with the other Shevatim). Therefore, it specifically mentions that Leah's children were born in Padan Aram, because that was the cause of them going to Mitzrayim, which is what is being discussed. The same answer is suggested here (kudos to Lee for this find).
(It may be worth considering that it may just be to remind us where they had come from now that they were going down to Mitzrayim from Beer Sheva, and it only needed to mention it by the first group. It also might have something to do with other people being born along the way, however, I prefer the above answers.)