Have to be careful now so it seems as for sure I will be monitored thoroughly now.
You bet you should. Your account is under searchlight now and you won't blame them if you're going to be honest with yourself. According to you, the site has a gambling prohibition notice on it. You're already breaking that law.
Did this happen to anyone else?
Nah, it hasn't happened to me.
In the first place, I wouldn't even use a site or an exchange that is clearly against what I'm doing. That's knowingly going against a set rule.
Would using an intermediary wallet to receive gambling funds be the solution?
No, I would use a private wallet for such.