Will using a tomato fertiliser hurt or damage herbs?

Tomato fertilizer is high in calcium and potassium. Herbs like high nitrogen fertilizer for foliage growth.

But, you can use the tomato stuff on herbs. It will be fine.

The topsy turveys do need to be watered almost constantly, so in addition to the upside down bottle, plan on watering everyday anyway. Tomatoes like evenly moist - not too wet, never dried out.

Some hardy herbs that will come back year after year are dill, sage, chives, mint.

The best fertilizer for all of the veggie plants is seaweed. You can get liquid or dry, you add it to a watering can to dilute according to package instructions and water from the top, feeding the plants thru their leaves about every two weeks. Fish emulsion works well too, but smells horrible.

Rosemary is hardy but grows into a very large bush over time. A good herb to plant with toms is basil, tho it grows large you can cut it often and it repels bugs from the toms.

Let's go with your questions first. Topsy Turvy needs more watering, because it's a container. It's not a manufacturing flaw, it's a container. Containers, by their very nature, hold but so much stuff and then the rest comes out. (You can't put 10 gallons of water in a 5 gallon bucket kind of thing.) So, yupper, got to water more often, but hey, impossible to over water, unless you water so much all the soil leaves. lol

Second different herbs have different needs, and most herbs have different needs from tomatoes. Tomatoes need water. If they don't get enough water, you'll know it. They'll split, rot, shrivel up, taste funky, and do all sorts of oddball things to you. But, hey, you already know that or you wouldn't be worried about watering. BUT there's a secret to all plants. Something to learn about a plant - Where does it come from?

I'm assuming rosemary is one of your herbs. BAD choice to stick rosemary above a topsy turvy tomato plant, or even near any tomato plant no matter how you grow it. Why? "Where does rosemary come from?" The Mediterranean. What's that like? Hot, sunny, and dry. That's what it likes. You got hot and sunny, but you missed dry. It just doesn't want as much water as a tomato plant. About 1/4th what a tomato plant wants.

Worse yet. How big does a rosemary get? Cute little plant, right? Yeah, this year, but it's a perennial. (And please note, tomato isn't and topsy turvy wasn't made for perennials, even if you grow them on top.) Rosemary is a bush. Think yew bush. Think small Christmas tree. Think evergreen, because that's what it is. Worse yet, take that back to where it comes from (Mediterranean) and you start catching on to potential problems. I am both a container gardener and have a rosemary. I'm also in zone 6. Being a container gardener changes the equation on growing plants. I should not grow anything that cannot withstand zone 5 winters. I do, but I just have to be careful. Rosemary won't survive if it drops to 10 degrees (which is does once every 5-10 years), so I have to protect her during those drops. If you live in zone 6 or colder, plant rosemary in a container that you can bring in a warmer environment for winter where it does get light, and it won't get colder than 20 degrees ever. And water her about once or twice a week in winter, and if you do put her where there is no heat, than only water when it's above 32 degrees, or you get frozen rosemary and kill her at her roots.) And, give her a big container eventually. She's cute and small this year, but she'll be a for-real bush in two years - shorter time, if you have no winters.

Also the soda bottle watering trick. Cute idea. Seems reasonable. A waste of time. It empties out in about 2-4 hours, so you're watering just as often as you were before doing it, unless you're fooled into thinking it works, so not watering as much.

Oh and fertilizer on herbs. Again, it depends on what kind of herbs, where they're from, and all the rest, but most herbs prefer normal soil, not rich, loamy, well fertilized soil. (Your ground sounds perfect for herbs already. lol) That said, we still fertilize our herbs, like we fertilize the rest of our garden, but only because we can't afford to change the container soil every year, so we just Miracle Gro food (which technically isn't fertilizer, but I'm going with that's what you really meant when you said fertilizer and it's such a small detail it shouldn't hurt to call it that) according to the directions. My fear is you're being too nice to your herbs, and it might cause problems, but we've always used mediocre soil for our herbs, so I have no idea what happens if you're too nice. And don't worry about your tomato, new container soil, so no added fertilizer needed.

And, most important, if the only reason you can't grow in the ground is because your soil sucks, then why not fix the soil? Amend it. That's the only difference between good and bad soil, unless your "soil" is like mine and it's really called "cement." (literally. We container garden because our backyard is a block of cement. lol) It's cheaper and gives you more space than getting terribly involved with container gardening before you know it. (I suspect you'll end up both loving it and keep making your garden bigger and bigger each year. You're starting the right way and already proved you're willing to learn. Be forewarned, gardening is addictive, and you're probably already addicted, because you will succeed this year - bar any inherited weird stuff with your tomato that isn't your fault like late blight.)

I wanted to answer your questions plus give you more. Topsy Turvy is a good enough product not to worry too much, but be careful on what herbs you choose for the top. Most herbs are perennials and take up a lot more space than anticipated when you buy those cute little things. lol