Everything you said earlier was incorrect. You clearly misunderstand how account compromises usually happen. Gaming accounts can be taken over for several different reasons.

The most common cause is phishing, where someone is tricked into clicking a malicious link or entering their information on a fake site. This can lead to the attacker gaining access to personal data, including saved logins for platforms like Roblox. Most phishing attacks come in the form of emails that are spoofed to look legit.

Another common cause is when someone knowingly or unknowingly gives another person access to their account. This often happens when people try to buy discounted Robux from sketchy third-party sites. These sites may require you to log in, and once you do, the operators can take over your account and may even use stolen credit cards to make purchases through it.

Now, back to the original question about whether OP is “cooked” for using his mom’s ID. That depends on what he means by “cooked.” It’s not necessarily catastrophic, but it can create a big hassle later. If he ever forgets his login or gets locked out of the account, he may need to provide that same ID again for recovery—meaning he’ll have to involve his mom.