While this might be blackmail, there are many possibilities for genuine good intents, too. Therefore, here's some more comprehensive thoughts on how one might handle unsolicited vulnerability reports. In short: you have every reason to be cautious, but you do not have to be rude.
Who may find vulnerabilities and why?
Ethical hackers perform their analysis based on a contract typically with predefined targets and limitations. These might be ordered assignments or more loosely defined bug bounty programs, either directly or through a platform like HackerOne. In any case, an ethical hacker (or a white hat hacker) always has an explicit permission.
From the details in this question alone it is hard to tell whether the message you got is a clear scam or someone with good intentions but lack of understanding – or willingness to adhere to ethical standards. The latter grey hats might even violate laws, but they do not have malicious intentions. The penetration testing industry is also extremely trendy, so there are all kinds of self-appointed penetration testers, ethical hackers, security researchers etc. with varying skills (or complete lack of them). In this case they may benefit from some gentle guidance, whereas false accusations might lead them to wrong direction.
I have found several vulnerabilities by accident, without an intention to poke the system in any way. These cases are usually rather harsh, and I do hesitate whether not to report it at all, report it anonymously, or report it with my name, which would give me the possibility to help them with further questions. The reality is that because I did not have a permission, the receiver may interpret or handle my report with unexpected ways, possibly causing me legal charges or other problems. So far, they have been sympathetic towards me.
Do you benefit from these findings?
You are asked to pay for the findings, but without knowing the details you cannot be sure whether they are worth paying at all. Vulnerabilities comes in all shapes and sizes. Some of them are critical, and some are minor. Some may also seem problematic from outside, but are completely irrelevant to you, or within your accepted risk. One simply cannot sell vulnerabilities in pieces, bundles, kilograms, or liters.
Two examples of completely worthless reports I have got recently, both with genuine intent.
A message suggested a reward for finding a web page protected by HTTP basic authentication, which indeed is not a secure authentication method. However, as it was only an extra layer of security before an actual login page, and not protecting any critical system anyway, it was not really a vulnerability at all. Therefore, the finding had zero value for the company.
A report of a missing SPF record. The explanation was correct and all, but the record was not missing! Instead of querying from DNS, the "bug bounty hunter" had used a web-based SPF lookup tool but used
http://example.com instead of
example.com. Due to this syntax error it did not show the record.
Therefore, in order to judge the value, some details of the vulnerability must be disclosed. If someone who has found the vulnerability thinks giving out these details may result in losing the reward, the vulnerability may actually be worthless: known, easy to spot with automated tools, within accepted risk, too minor, or otherwise irrelevant. On the other hand, if the vulnerability is severe, it is often also so complex that giving some proof of concept will not completely help fixing it. The additional work required to describe and address the vulnerability is valuable and will be paid.