I don't know specifically what your flowers are, but I have a number of perennials and wildflowers that do this. It's perfectly normal. As the summer goes on, they get tall, and, especially after the flowers bloom, become top heavy. A hard rain, or sometimes a wandering raccoon or skunk, will bend them over to the ground.
I can't see clearly in these pictures exactly what your supports look like, but bringing the plants up gently and supporting them with minimal breakage is the goal, and, as Srihriri Yamanoor said, you're doing a great job! They look really pretty against your fence so I can see why you like them.
Going forward, make sure to check on them regularly, and, if the bunch gets wider, loosen or rearrange the supports. That will continue to keep the supports themselves from breaking the stems. Once they're in full bloom, or if the flowers are too crowded, you can pick some and put them in water. Again, I don't know exactly what you're growing, but many summer wildflowers will last nicely inside at least for a few days. In fact, all the flowers I see in your pictures would make a very pretty mixed bouquet.
When trimming, cut back to the next joint where the little branches meet. You might see a new flower starting at that spot, and taking off the older ones helps that bloom. If they're really unruly, you can cut them down farther than that, or even thin them by cutting some off at the base. I myself prefer that crowded look with flowers everywhere in random patterns!
I also agree it's important to be careful when watering. You may already be doing this, but make sure to set your hose on a lower setting (if it's adjustable), and point it at the base of the plant, rather than at the higher sections, and definitely not from above. I've knocked over many a tall flower by turning my hose pressure too high, or aiming it at the wrong spot!