Actually I use all three methods. I mulch my garden with straw and eel grass to retain moisture and add organic matter. I have a bin constructed of hardware cloth that is about 40" in diameter. I put stalks, leaves, and limbs in it. Sometimes I move contents from the bin to the tumbler after emptying the tumbler. The tumbler gets kitchen waste mostly. I put a few shrimp shells in it about once per month with no problem. It is full of worms and beatles but they are not earth worms.
The tumbler lid has positions for open, vent and closed. Will set it to vent in future. It also has drainage holes in the bottom.
I live on the Outer Banks of NC. Our soil is 100% sand unless something is added. My garden soil has benefited from the addition of a truck load of topsoil, plus five years worth of compost, peat moss, chicken manure, ground peanut shells, and eel grass. I also have a drip irrigation system. I get an annual soil test from NC State University. My fertilizer requirements are normally 6-6-18, which is often used by tobacco farmers. Lime is not needed every year.