Neal ...
>>>>in spring found that rodents had been living and nesting under the layers, and had fattened up on Lily bulbs too.
From what I have read, my ground doesn't freeze, this is the only reason for holding off mulching until after the first freeze. The rodents have found other places to over winter than your mulched beds.
Putting down mulch after the first freeze is not going to impact soil temperature that quickly, but waiting forces rodents and such to find different places to keep warm during the winter.
Works for bears and yellow jackets, too ...
Smiles,
Lyn