Take it for what it is worth from Wiki, I am no expert,
"Annealing, in metallurgy and materials science, is a heat treatment wherein a material is altered, causing changes in its properties such as strength and hardness. It is a process that produces conditions by heating to above the re-crystallization temperature and maintaining a suitable temperature, and then cooling. Annealing is used to induce ductility, soften material, relieve internal stresses, refine the structure by making it homogeneous, and improve cold working properties.
In the cases of copper, steel, silver, and brass this process is performed by substantially heating the material (generally until glowing) for a while and allowing it to cool. Unlike ferrous metals--which must be cooled slowly to anneal--copper, silver[1] and brass can be cooled slowly in air or quickly by quenching in water. In this fashion the metal is softened and prepared for further work such as shaping, stamping, or forming."
I think too that is what is done with rifle and pistol cases to soften the case mouth to keep it from hardening and cracking with reloading.
As I remember from my little metallurgy experience, quenching hot steel in water or oil usually resulted in a harder surface, but you need to realize what it is going to be used for after doing that. If you are making punches that is fine, but if you are making gaskets, maybe it is not so fine. But in the case of Copper, it sounds like either method works.
Dave
69S