Someone called me to ask whether I have recharged (added money to) my mobile account. He told me that he was calling from the network provider and wanted to assist me with the recharge. Unlike an automated call that I usually get, this was an actual person who was calling, and I had not even contacted their customer care or anything. This left me a bit suspicious and after checking the number later in a website, I found that there were a lot of people who reported that number to be scam.
However, I do not know how someone can scam people by knowing just their mobile phone account details. Is there any scam like this or am I just overreacting?
If you mean "recharge" as in add more money to your phone payment account, then this is 100% a scam. For the following reasons:
The phone provider will most likely not call you asking for personal details to apply a payment. Even if they did call to tell you a payment is due, it would either be an automated message that says "your payment is due" or they would call and only have to verify the information they already have on file.
This sounds exactly like scammers calling you and saying they are from "Microsoft" and want to help you renew your Windows subscription. Usually they make you buy some gift cards and send them the numbers.
You looked up the phone number and many people have reported it as spam/scam.
If you want to be sure your phone account is in good standing, look for the main customer service number online and speak to them. Do not call back the number that called you originally.
EDIT: This is from my own experience in the USA. I don't know if providers directly calling customers is more common in India, where the OP is from.