It is sometimes very difficult to know what they are up to. Just some things that come to mind since it seems, per your statements, you are new:
Are there any instructions anywhere in your emails that state you need to click on anything to confirm something? (Double-check your SPAM folder too.)
Did they state they are sending you anything in the mail?
Are you located in a country that you can have adsense in?
Did they send you a text message that you need to confirm with a code or anything?
Are you expecting an automated phone call from them with a code to confirm anything?
Were you ever banned from it in the past? (If they ever ban you, they ban you for life.)
Also keep in mind that those welcome-type emails are auto-generated by email auto-responders that are set to send at a specified time and aren't necessarily linked to your account status.
I have read a lot with those who did nothing wrong and were banned, but I am still using it with the hopes that nothing will happen. So far so good and I'll continue to be careful. Best of luck!