Have heard all sorts of recommendations for the Topsy Turvy but none based on personal experience yet so haven't tried them.
I've done upside down tomatoes for years. I currently have 40 toms growing upside down in two 50' planters with herbs, peppers, strawberries, and greens growing upright from the tops. Don't ask. There's issues but the sales pitch is pretty accurate. You avoid soil born diseases and you don't need to bother with staking or cages. You should grow a determinate tomato as indeterminates need more care and soil over a long growing season. They can also reach the ground very quickly. A planter type determinate is ideal, but pretty much any determinate works. Celebrity and Ace are fine choices for medium to large fruit. Park Seed's Tumbling Toms are cherries marketed specifically for upside down growing.
The biggest issue is water leaking onto the plant causing the main stem to split reducing yield dramatically in some cases, killing the plant in others. It's especially damaging with liquid ferts. Food grade sponges wrapped around the stems inside and out prevent this. Branches will reach upward and sometimes break off if they're very thick or bear fruit early. Nipping the first dozen flowers in the bud pays off in the long run. Starting with a leggy plant actually seems to produce a little better yield (burying most of the plant inside the pot on transplanting), which is great for those starting seeds indoors (which are usually much leggier than nursery stock). I wouldn't use the Topsy Turvy unless aesthetics was important though. A five gallon white bucket, drilled in the bottom, is a better growing container, cheaper too, but diy things appeal to me. Another issue is the soil can get a little too warm hanging in the sun and the plant will suffer in hot climates. This is another plus for a white bucket with a lid to seal in moisture. Though you need some evaporation or you get mold. There are ways to shade the soil container, but most are ugly. It's in cool climates where the extra soil warming produces the advertised (great) results.
Do you use a regular bucket or a more "narrow" bucket like the topsy turvey?
Regular five gallon paint bucket, sterilized. Brand new or food grade buckets from a restaurant may make some more comfortable but the plastic-phobiacs are going to protest regardless. I like the paint buckets because they have both a big lid and a screw on cap.
This is close to perfect. Growing the transplant upright in the soon to be inverted container for a week or two helps the plant in several ways. Mostly, it allows you to harden off a nursery (likely greenhouse) plant to your conditions. You can gradually expose it to more sun this way, which is key to the hardening process. Roots definitely perform better over the growing season with a week or so right side up after the transplanting regardless of hardening off. I add sponge surrounded by peat to the planter hole. I don't trust the wire handle to do the job all year, but it probably would. Still I drill three holes evenly around the lip for a small chain or rope. Since I ran these along sloping eaves with a southern exposure (hideous looking but I'm divorced so who cares), the rope/chain allowed me to adjust height easily. In the case of big indeterminates, I've had them hanging down 20 feet by the end of the year with ropes pulled tight to the roof. Fwiw, the 40 inverted toms described in the quote is (a 120 plant hydroponic technique test and) in harvest. It's in a greenhouse that has unleased space to play with. The 40 upside downs were grown soil-less with hydroponic drips, 40 more in a simple aeroponic setup, and 40 identical plants upright in industry standard (NFT) hydroponics (control group). These plants will produce through September unless we pull them early, and right now the upside downs are by far the least impressive. I doubt they can ever catch up and will fall further behind. The intercropping of herbs and veggies in their tops will not produce enough to make them worthwhile. They probably need larger planters, but I'm disappointed.
As for growing something in the soil above the bucket, lawn grass has been a great way to keep tomatoes happy for some green thumbs. Grass loves nitrogen which can stunt a tomato's yield. So you can happily hit the planter with a cheap balanced triple sixteen fert or 20-20-20 and know the grass will use excess nitrogen leaving the toms with good conditions for a heavy fruit set. Toms prefer an even water supply and the grass does a great job keeping things evenly moist. If you over water the grass sucks it up and grows. If you underwater the grass keeps the soil moist longer than any mulch as it slowly dies back. Most pottig soil is a touch acidic for grass, so a sprinkle (a half cup) of wood ash balances that for happy grass and provides calcium for the toms. The person I know who has great results doing this cuts the grass sod-style right from her backyard. No seed. Just plant the tomato. Grow it upright for a week. Invert and hang. Add homemade sod to the top, water, fertilize, Mow with scissors.
GL