How do I keep my beads from turning to the back of the stitch?

You're acutally already doing the main fix, which is pushing the bead back against the hook before you pull through. The reason you're still getting flippers is that the bead also needs to be sitting flat against the hook, bead hole facing the direction you're pulling, when you do that. If it's angled even a little, it'll rotate as the stitch tightens.

Tension helps but it's not the whole story. With cotton thread on a 1.5mm hook, the bigger issue is that cotton has no stretch and no grip, so beads slide around way more than they do on wool or nylon. A lot of bead crocheters use a thread with a bit more tooth for exactly this reason. If you're sticking with cotton, slowing down and consciously placing each bead is the way. On orientation: with seed beads it matters less than you'd think because the hole runs through the same axis either way, but what does matter is wether the bead slides to the front or back of the loop before you catch it. Beads migrate along the strung thread as you work, and ones sitting at the wrong spot when you go to use them are the ones that end up backwards. Some people will flip a bead deliberately on the thread before the stitch if they feel it sitting wrong. Before you rip anything back, try this: after you pull through with the bead pushed forward, give the working thread a gentle tug while pinching the base of the stitch. That locks the bead into the front loop before the next stitch can shove it around. Once it's locked in place it genuinely can't flip. And honestly, a crooked bead every few stitches in round three or four of a first bead project is normal. My first beaded bag looked like the beads had been applied by someone shaking the work violently. If you're still getting hidden beads after trying the pinch-and-tug, then yeah, go back, but I'd finish the round first and see if the fix holds.

That pinch and tug trick is real, it's what finally got my beads behaving after two rows of chaos on a little amulet bag I made. The thing that made it click for me was doing the tug on every stitch for a whole round, even when it felt unnecessary, til my hands basically learned the motion. After that I could skip it on most stitches and only use it when a bead looked like it was sitting funny on the hook. Also worth checking your beads aren't mismatched sizes, I had a handful of slightly larger ones mixed in and those were the exact ones flipping.

Wait, so you have to put all the beads on the string before you even start? I always assumed people sewed the little beads on after the pouch was done, like decorating a finished thing. The idea that every single bead is allready sitting on the thread waiting its turn kind of blows my mind. Also the part about sliding the bead around before each stitch sounds fiddly with tiny beads. Is there a tool that helps with that, or is it all just done with fingers?

Update: the pinch and tug thing fixed it. I forced myself to do it on every single stitch for a full round, even when it felt pointless, and after that my hands just picked up the motion. I also started making sure the bead lies flat against the hook before pulling through, which was the part I was missing. Only had to rip back one round, not three evenings of work, thank goodness.