It's definitely easier to have someone leave for non confrontational reasons in a month to month (selling, renovating, etc) but from an eviction standpoint there are a lot of variables.

I just want to make quick work of it - not sure if there will be a confrontation...I just want to be in and out and not have to worry about botching the locks in the process.

The existing tenant witnessed a transaction take place out front of the building.Those are all the details I have.Should he confront the new tenant?

No specific confrontation or antimosity.  

COnfront this PM, and get rid of them.

My question is - should I confront the tenants about their statements?

As a rule, they don't like confrontations.  

the story starts in January of 2016, when i added a tenant to my one family house. 10 days later she decided to move her stuff in. she rented a one bedroom in my house and was bringing in her belonging that could fill a fill 1 bedroom apt. when she didn't have enough place to put her stuff she began to leave everything in the living room. when i confronted her about it, she began to act threatening and irrational. i thought "hey she is stressed. let her cool down. the following day i tried to talk to her and she really lost her mind. i told her "it was not going to work out and she had till the end of the month to find somewhere else to leave.

That way I immediately see that a payment has been posted, taking that one point of failure out of the process.They can schedule payments and you can request if you do not see it electronically too keeping the direct confrontation out of the picture.

Thomas S.I agree with Greg,I would send him notice of balance due on his rent,  for rent owed, you don't carry forward back rent because someone(TRA) paid current rent on his behalf, he's still responsible to make sure his rent is current and no balance is due.If he doesn't remedy the situation or ask his TRA to come up with the funds he needs to stay in the unit, then I would proceed to file for eviction.Don't confront him by yourself, take someone with you if you have to deliver notices, And at the least I'd give him proper notice of non renewal when that comes up, even if he pays what is owed, at least then you'll have a head start in ending his tenancy.Check your local state laws for eviction proceedings, and non renewal notices.