Second, I let the tenant know I know their criminal history and tell them to leave.

Although, for it to be a criminal trespass.. something that will actually hold up, he would have to be present with the police there.

For example, I mention that every adult must pay a $30 application fee, pass my credit/criminal background, make a combined income of 3x the rent, and whether or not the property accepts pets.

Every adult should be fully screened to ensure you aren't renting to a violent criminal, drug dealer, etc.

But wouldn't this be criminal not civil?

Think hard about your criminal background criteria.

However, if that effort fails, the local agent is equally liable – criminally and civilly – for any fees, fines, etc. associated with the property." 

How else would you know which one is the criminal?

Once you start processing the credit/criminal, the money is spent, and you can't get it back.

For example, I mention that every adult must pay a $30 application fee, pass my credit/criminal background, make a combined income of 3x the rent, and whether or not the property accepts pets.