Julie
I”ve not used ‘tumblers’ as such, but I did experiment this winter with a rigorous regular turning of half ripe compost for 6 months which has now matured beautifully – still a few worms in it but it is truly crumbly and soft. I used the high tech implement known as a garden hoe, going down as far as possible, lifting sideways and then spreading the high side down into the cleared side to mix. As the weeks past I could get deeper and deeper and of course this helped with the aeration. I was doing this in a PVC 0.2 cubic metre compost bin which was about 2/3 full at the start and has now reduced down to about half full.
On the basis of this, I can imagine that tumblers will work but if you are time rich but cash poor, maybe using hoe and fork may be a low cost solution?