Here is the ull code section and not the snippet:
O.C.G.A. 16-5-90 (2010)
16-5-90. Stalking; psychological evaluation
(a)(1) A person commits the offense of stalking when he or she follows, places under surveillance, or contacts another person at or about a place or places without the consent of the other person for the purpose of harassing and intimidating the other person. For the purpose of this article, the terms "computer" and "computer network" shall have the same meanings as set out in Code Section 16-9-92; the term "contact" shall mean any communication including without being limited to communication in person, by telephone, by mail, by broadcast, by computer, by computer network, or by any other electronic device; and the place or places that contact by telephone, mail, broadcast, computer, computer network, or any other electronic device is deemed to occur shall be the place or places where such communication is received. For the purpose of this article, the term "place or places" shall include any public or private property occupied by the victim other than the residence of the defendant. For the purposes of this article, the term "harassing and intimidating" means a knowing and willful course of conduct directed at a specific person which causes emotional distress by placing such person in reasonable fear for such person's safety or the safety of a member of his or her immediate family, by establishing a pattern of harassing and intimidating behavior, and which serves no legitimate purpose. This Code section shall not be construed to require that an overt threat of death or bodily injury has been made.
So, your course of conduct apparently placed one or both of them in reasonable fear for their safety. At least, that appears to be the premise the police were operating under with the arrest and is likely quite a reasonable assumption under the circumstances. And, as I said, since the police need only the minimal burden of probable cause, the arrest can be made without complete certainty as to the full details or without conclusively determining your intent.