Salam Union.
Thank you for your good questions which helps the more elaboration of the issue.
Muhammad Jamil humud Al Amili has said in the introduction of his book that this idea is only said by himself and other Shia Ulama(scholars) do not believe in it.
Also, after searching about his book, I found that according to the saying of Shia great Ulama(scholars) his book has not any scientific value.
Please follow my post for more elaborations:
1.There are discords between Shia Ulama that, are all parts of the Tafseer book of Ali ibn Ibrahim( a great Shia scholar ) for himself, or there are some additions from his student, Abbas in Muhammad Qasim, to the book of Ali bin Ibrahim. In addition, it should be said that Abbas ibn Muhammad Qasim is indeed unknowm and we do not know he is relaible, or not. So, this quotation from the Tafseer of Ali ibn Ibrahim Al-Qomi is not valid.
In addition, Abdurrahiim Al-Rabbanii Al-Shiraazi( a Shia scholar ), the researcher of Bihar Al-Anwar, says:
فيه شناعة شديدة، وغرابة عجيبة، نستبعد صدور مثله عن شيخنا علي بن إبراهيم بل نظن قريبا انه من زيادات غيره، لان التفسير الموجود ليس بتمامه منه قدس سره، بل فيه زيادات كثيرة من غيره، فعلى أي هذه مقالة يخالفها المسلمون بأجمعهم من الخاصة والعامة وكلهم يقرون بقداسة أذيال أزواج النبي (صلى الله عليه وآله) مما ذكرـ
The saying of such bad things is far from our Sheykh, Ali ibn Ibrahim. Rather, I think strongly that it is indeed the addition of others in his book. Because, his avaliable Tafseer book, is not all of its patrs from him(Qoddisa Serroh). Indeed, there are many additions from others in his book. Anyway, all the Muslims, either Shia or Sunni, oppose this saying(the saying about commiting of adultery by Aesha), and all of them have asserted to the chastity of all the wives of Prophet(sawaws) from Adultery.
(Source, Bihar Al-Anwar, V.22, P.241)
2. Allama Majlisi( a Shia scholar ), the auther of Bihar Al-Anwar, siad that, based on Aql(reason) and Naql(Quran and Hadith), this saying about Aesha is not valid.
(Bihar Al-Anwar, V.32, P.107)
So, the issue you mentioned is unvalid and has not any scientific value.
1. The Isnad( route of the narrations ) of this Hadith is not Sahih, rather it is indeed Mursal( one of the kinds of un-Sahih, i.e. unauthentic Hadiths ). Isnad of Hadith is,
عَلِيُّ بْنُ إِبْرَاهِيمَ عَنْ مُحَمَّدِ بْنِ عِيسَى عَنْ يُونُسَ عَن رَجُلٍ عَنْ زُرَارَةَ عَنْ أَبِي جَعْفَرٍ
Ali ibn Ibrahim narrated from Muhammad ibn Isa, who narrated from Yoonos,
who narrated from a man, who narrated from Zorara, who narrated from Abi Ja'far(a.s.), 'the Hadith'.
(Usool Al-Kafi, V.2, P.402)
As the Isnad( the route of the narrators ) shows, the narrator who is between Yoonos and Zorara, is not known. So the narration is not authentic and has not any scientific value.
2. Regardless of authenticity of the narration, 'Al-Fahisha' which is used in the narration, does not mean 'who has commited adultery' in this case. Indeed, Al-Fahisha in this case means, who did not act according to the right and what Allah has ordered.
Ibn Manzoor wrote in his book, Lisan Al-Arab, different meanings of Al-Fahisha and he wrote also,
وقيل: الفاحشةُ خروجُها من بيتها بغير إِذن زوجها.
It is siad, 'Al-Fahisha is a woman who comes out from her house without the leave of her husband.'
(Lisan Al-Arab, V.6, P.325)
According to Sunni authentic narrations, Prophet(sawaws) ordered Aesha not to come out from her house due to fighting against Imam Ali(a.s.). But she didn't do this order of Rasulallah(sawaws) and fought againts Imam Ali.
Haakim narrated a tradition with an authhentic route of the narrations that Prophet(sawaws) warned Aesha and said to her that not to come out from her house due to fighting against Imam Ali(as). See,
Mustadrak of Haakim.
Ibn Manzoor also wrote in Lisan Al-Arab,
وكلُّ أَمر لا يكون موافقاً للحقِّ والقَدْر، فهو فاحشةٌ
And any doing which is not based on the truth and the order of Allah, is indeed Al-Fahisha.
(Lisan Al-Arab, V.6, P.325)
Also, according to a narration in Sunni authentic books, like Sahih Muslim, Prophet said to Aesha, 'do not be Al-Fahisha', in which, Al-Fahisha means, who uses harsh words. See
here.
So, 1) the Hadith which is in Usool al-Kafi is not authentic; 2) the term Al-Fahisha in the mentioned Hadith does not mean commiting adultery.
Unvalid saying which doesn't have any scientific value.
As I proved, according to the beliefs of Shi'ites, Aesha never commited adultery, either when Prophet(sawaws) was alive, or after the demise of Prophet(sawaws).
Good luck!