Your experience with the stray sounds exactly like what is going on in my yard! I feed approx 6 to 8 feral cats every day. Ally, who was a rescued feral kitten, tolerates them all, except one.
This beautiful pitch black female with eemarld eyes (she is stunning) will come and eat, and then sit and STARE at Ally for ages. It's like she just liked to wind Ally up! Of course Ally eventually loses the plot completely, and launches herself at the window while growling hysterically. Her whole body goes spiky too!