I lived there for 5 years and never once saw anything like that.
Really, you should have gone for a walk in the other direction more often ;-)
But seriously it is very rare in the centre of Calis, the the turkish family living in the old white bungalow opposite the Sunday Market used to carry out this ritual.
The law changed sometime ago approx 2005 whereby the animals had to be taken to a specified location, however, some families of the old school prefer to still carry out the ritual in their own grounds. Fethiye council set up the site of the Tuesday market as a Kurban Bayram abattoir, at this time the flow of the river from the market to the sea ran red.
It is a traditional custom, respect it and get on with it.