The sentence ending particle (終助詞) もの and its contraction もん are used to give an explanation accompanied by some sort of emotion, in informal register. It is used a lot, but not exclusively, by kids. It can also be used by people, a lot of times females, to play cute.
For a rough outline of its usage and how to form sentences with it, see this:【JLPT N2】文法・例文:〜もの / ~もん / 〜んだもん
(三省堂)『大辞林 新装第二版』により:
不平・不満・恨み・甘え・訴えなどの気持ちを込めて、相手の自分に対する非難に対し、根拠や理由を示し、反駁する。「だもの・ですもの」の形をとることが多い。
That is the usage in your linked post. However, it is not quite the same as how this phrase is used in your sentence. There is another usage that is pretty common in daily speech too but is often omitted in grammar explanations and JLPT materials. I wanted to preface this answer by giving the JLPT side of this phrase first because that's the usage you are more likely to encounter in textbooks and class.
It is also interesting to note that this usage seems under-documented and under-explained. I have checked several dictionaries, and most simply lump it together with the other sense under 「理由を述べる」or「理由を示す」, but it is actually more than just giving a reason. This sense, with ね or な, is used to express agreement, to echo what's said, and in a way to help the other party in the conversation by saying, "Oh yeah, that's true, because..." Rather than seeking agreement, it gives agreement.
(三省堂)『大辞林 新装第二版』により:
(「ものね」「ものな」などの形で)詠嘆の意をこめて理由を表す。「でもあなたと私とでは考え方も違いますものね」「なるほど、それは彼のお得意だものな」
(大修館書店)『明鏡国語辞典 第二版』により
終助詞「な」「ね」がつくと、相手と同調する気持ちが伴う。
This phrase is often used together with 「なるほど」「確かに」, as is in your case. As an example, this is from a conversation I had with a Japanese friend yesterday. It just so happens this phrase popped up in our exchange.
俺:ウサギの足は多分古い迷信だと思います。昔話でしょう。
友人:確かに流行ったのも80〜100年前らしいですもんね。