Practice pitching, especially longer pitches to a target, with less brakes or spool tension than you're comfortable with. This will force a reaction from you at a pace that's different and slower than while overhead casting. An overrun is also less dramatic during pitching as everything is slowed down. You'll have more time in which to process what's happening. You'll find, rather quickly, that improvements here will translate during regular casting.
All braking systems require the spool to be spinning to actuate them, or turn them on, but there are some important differences between how magnetic and centrifugal braking systems actually work. Understanding these differences may help to shortcut your learning curve which will allow you use less braking.
Centrifugal braking, as found in most Shimano reels, relies on mechanical friction which is practically instantaneous. The moment the spool spins the brake arms are engaged with the braking surface. In some cases this is a brake drum or race, and in others it's a thrust plate. This is why it's generally understood that centrifugal brakes are more effective at the beginning of a cast.
Magnetic brakes as employed in fishing reels are unusual in that while there are magnets present, the moving part, the spool, is not magnetic material. In other words, a magnet will not stick to your reel's spool. This system requires motion to generate a magnetic field. The faster the spool spins the greater the field, or more magnetic force. This is a simplified explanation for the purposes of this exercise. Looking up "Eddy current braking" will further your understanding here.
The bottom line is this: Unlike centrifugal brakes, as found in Shimano reels and others, that "turn on" fast, magnetic brakes "turn on" slower. This is especially true when the spool is farther away from the magnets. The dial on your Daiwas moves the magnets either closer or farther away from the spool's inductor ring. The deeper the inductor ring is inserted into the magnetic gap the more magnetic force is present, but only when the spool begins spinning, and increases with spool speed. But, there's a slight "lag" before force is applied. There's very little magnetic force "present" at the beginning of the cast. It ramps up with increased spool revolutions. This is why an instantaneous backlash is likely if you whip a cast with a Daiwa reel. There are essentially no brakes "on" for a split second. The upside here here is that a harder cast is not necessary, and is actually counterproductive.
Understand that you can cast hard with a Daiwa reel, but, there are subtleties involved in unloading the rod as you launch the lure. Any jerkiness during that process can result in a quick backlash or a mid cast fluff up just before the apex of the cast. Mono is more forgiving in this scenario and may self correct, or sort itself out. Braid will usually just wrap around the spool resulting in a backlash. This is why people describe a "lob' or a "sweep" cast when explaining transitioning from a spinning reel to a baitcaster, especially one with mag brakes.
You'll have to learn what this feels like while your thumb control increases. As you get better at feeling the rod load then unload during launch without jerkiness or a bounce, you'll be able to go farther down on the dial which will increase your casting distance without incident. You'll also find out that not much thumbing, if at all, is required in the middle of the cast where the mag brakes are most effective, just slightly in the beginning on power casts. If fluffing does occur midcast your thumb will kick in automatically. However, a minor adjustment of the brake dial or a slight dash of spool tension should tame those without sacrificing much distance at all.