"Garden soil" is generic dirt. Can't understand why anyone sells it, except for people who don't have a yard of generic dirt. And to rip off everyone else.

Your tomatoes will grow, but bed soil compression and water management will be an issue. I guess if the plants aren't too big already, and you want to spend a large bundle on container soil, you can go ahead and make the switch. What you could do, if the plants are small, is to scrape out the soil around the periphery of the container, and replace it with a suitable container mix. Put that container mix on the top as well, if there is room. If you do that, things will work out OK.

I've seen tomatoes grown in containers using 'black earth' topsoil. They did fine. Maybe not as 'fine' as proper container medium, but acceptably fine.

For a very seasonal, short term crop like tomatoes, you can get by with the garden soil although you will have to pay very close attention to watering as the drainage of this type of soil for use in containers makes it far too easy to overwater and with a very high PWT. For anything being grown longer term, I would suggest repotting in a proper container soil.

btw, bagged "garden soil" is not really the same stuff as you would dig out of your existing garden. It generally has a much higher level of organics and some drainage enhancers like sand in addition to a small amount of screened topsoil or loam. It is intended as a soil amendment, not a stand alone product.

You could improve it a bit by mixing/adding coarse perlite; poke around with a chopstick to get it mixed. By as gardengal suggested, you should be OK if you pay enough attention to watering

Thank you all for the advice. I looked into mixing in perlite, but the bags were so small that it would've ended up costing me more to buy enough perlite for each pot than to just buy a few new bags of potting mix. If the tomatoes got more sun, I would've been more willing to leave the garden soil and watch my watering, but they don't get as much sun as they should, making it even harder for the soil to dry out. So I ended up repotting them all. They were still small enough that I was able to pop them out easily. The root ball on one was too wet that it kind of fell apart when I lifted it, but hopefully all will be good.
Now the challenge is figuring out how to get them enough sun, as no one spot in my yard gets a full 6 hours. That's why I chose to plant the tomatoes in containers this first year, so I can move them around as needed. I'm hoping when the sun gets a little higher in the sky as we move into summer, it'll be above the trees now creating shade and I'll pick up a couple more hours.