The float in the tank stops the water right at the brim of the siphon tub. There must be some surges with the water that causes a little to drain over the tube. Then the float begins to fill the tank the 1/2 inch of water that escaped. How do I adjust the float just a little?

All floats can be adjusted but if you can attach a picture of yours or name the brand we could give specific directions. Old time brass rod unit you could just bend the rod by holding each end and bend slightly arching up. Newer units frequently have an adjustment screw on top of what looks like a tower. What's yours look like

If 1/2" water "escapes " it sounds like 2 issues, leaking flapper and float too high. You go through the phantom flush and fill cycle and it wastes water and costs you money. As soon as the water reaches the top of the fill tube, turn the supply valve off and watch. Tell us what happens.

What type of ballcock do you have? Tonight, before bedtime. Place some food coloring in the tank, Next morning check the bowl for color, Let ne know what you find. Good luck, Tom