No, plots made using your farmer public key and pool public key and sold to you as a service, are safe for you to use as these two public keys are public by definiton, they are linked to your private key, which is not revealed to anyone, unless you reveal it.
Buying a ready made farm is more problematic. You can only farm someone elses farm by having their private key that the plots were made with. They can have a copy, either written down, on a computer or just memorised. I am told that’s okay if you set the farming rewards address to the public receive address of a second “cold” wallet that you own, a second private key that you create with as much attention to it not being stolen by malware etc as you can manage*. then store offline. Any reward is instantly sent to your cold wallet, and cannot be stolen by the former owner. However, I am not 100% convinced of this, it sounds too easy.
*Some people might do this on an entirely new computer which should have had no risk of being compromised, I just installed Chia on a machine I have not used for any crypto related activity. Created a key, saved the mnemonic safely offline (paper printout for example), copied the public receive address, then uninstalled chia and deleted all reference to chia anywhere on the machine.