As far as I can see, we can only say that possessor-possessee is mostly reliable, but not 100%. This is based on:
The order of possessor-possessee is strongly preferred, however, and should only be reversed in cases of overcrowding, or for honorific transposition.
If I have understood everything correctly, it's because 'azantyssy' is nominative whereas 'annī' is accusative, so that it's unambiguous that 'Azantyssy' is the subject, and 'annī' is the object in this sentence. 'The men's knights find the horses' would therefore be 'Valoti azantī annī rhaenis.' or 'Azantī valoti annī rhaenis.' (Which would then be truly confusing)
as you said correctly, "azantyssy" is the nominative. in your sentence "the men's knights find the horses", "knights" is the subject (nominative), so it would be "valoti azantyssy annī rhaenis" (strongly preferred word order, see sprightBark's comment) or the ambiguous "azantyssy valoti annī rhaenis" (not recommended for this translation). the question was not about what's the subject of the sentence, but about whether "valoti" (gen.) refers to the subject (nom.) or the object (acc.) of the sentence.