There are so many salvias... that there is no one correct way to treat them all.
The safest approach is to leave them alone. I have a nice patch of salvia coccinea that often returns from last year's plant... and even when It doesn't, I still get lots of babies from last year's plants.
People that insist on a tidy garden... Never get returns of salvia coccinea.
salvia microphylla on the other hand... Is very forgiving... You can do anything you like to it...
and... Salvia guaranitica is also pretty bullet-proof.
But there are so many different salvias, many varieties that I haven't even tried yet...
There are salvias that are annuals, and additional perennial salvias that can not be disturbed... as well as varieties that simply aren't winter hardy here ever.