Hi Jocelyn,
Congrats on the first investment property! How long is the lease term for? If it's month-to-month and you truly don't want that person in there after hearing this, then just reach out to them to tell them that you will be terminating their leave in the upcoming month. If it's a longer lease, then I would keep a close on eye on their behavior and use one of the clauses in the lease as a reason for termination if they break it. Completely legal if your lease is set up correctly.
Couple of other thoughts....
1) How did the tenant screening process go? If you did your due diligence, then the tenant should not be a problem. Was there anything in his background check that threw you off? Anything from the last two housing references? from the work reference? If you didn't do any of these things, make sure you take it as a lesson for future tenant searches. BP has great content for finding good tenants. I would recommend the BP book on Rental properties.
2) How much do you trust this "someone"? They could honestly just be an ex trying to ruin this person's life! If you trust them, then fine take it as a reasonable warning. If not, then why be so concerned? I would just continue to closely watch the tenant and trust your tenant-screening instincts, there is a reason you accepted this tenant.
Best of luck! Great learning opportunity here.