This is the first time I've ever heard the term "second puberty". Searching online it seems people do use that term. When you read things like this, you have to keep in mind that there's a lot of poor and inaccurate information available online. Like, if I google search "how to target belly fat" you'll find plenty of articles telling you how to do this, when it's impossible to spot reduce fat. The problem with online information is it's not peer reviewed and anyone can post anything. And when you "hear people say" things, they're often just regurgitating things they've read online or heard people say.
As for your question, I'm not an expert on women's hormones, but I'm thinking this isn't totally accurate. Women for sure will go through hormonal changes just before menopause but that won't be in your 20s. Sure, there will always be some people that have a form of medical issue, but for the vast majority, it will absolutely be lifestyle changes that cause weight gain in your 20s. Even if your hormones were to change, you still cannot gain body fat without a calorie surplus. You can't build a thing (fat) out of nothing. If you maintain your healthy diet and exercise, you have nothing to worry about.