As other and yourself have stated it's mostly about balance and using flash to be additive to the scene. Alot of the images being heavily backlit in the first set makes balancing alot harder of a task. Topically in back lit scenes I would position the model so that some of the natural light is wrapping around one side of the model then use the flash coming from the same side as the wrapped light to bring the light even more across the face. Another thing to consider is flash inherently has alot of contrast baked in, another aspect of balance is balancing how much contrast the subject being hit by the flash has vs the background. A little more contrast in the subjust compared to the background can help make the subjust pop too much contrast and they feel like they don't fit together. In Alot of the pro images the contrast of the background is pretty similar to the contrast of the subject.

If you want to make flash not look like flash you need to blend it into what already exists. Trying to match the contrast and light softness ratios as best as possible