Neighborhood dispute with my tenants

[Hugo Uriostegui]

I recently started renting out my first property, I own the house and the land. On the contract I allowed pets inside the house for a fee and a security deposit of 450. My long time neighbors called me stating that my tenants dog got out of our fenced yard and damaged his property and animal. I was in a rush to rent the property due to me getting a job out of state, I didn't think about switching from owners insurance to renters insurance. My question is can the neighbor come after me the owner for the damages caused? He called me himself and is starting a civil law suit against my tenant and myself by being the owner? The property is located in the state of Florida, thank you in advance.