Maybe some additive in the detergent you use becomes photosensitive when oxidized by bleach . That sort of reaction is rare, but it can happen.
Here in the northern hemisphere, I’ve hung bleached whites out in the sun and they don’t turn purple, so it’s not just something that bleach and cloth do when you hang them outside. There must be another factor, such as your laundry detergent, involved in the purpling. You might try contacting the company that makes your soap and asking them if they know what’s going on.
This may be a different phenomenon, but detergents typically have anti-yellowing ingredients that fluoresce blue in UV. The idea is that ambient light will cause just enough blueish glow to cancel out the natural yellowing of the fabric, so it looks white.
Bleach, though? I dunno about that, unless it’s just removing some of the yellow, making the blue more obvious…
The brighteners are to conceal the last bit of yellowing the bleach wasn’t able to remove. They just overdo their adding of blue in direct sunlight. But I can’t say why the color disappears. Perhaps some of the fresh brightener gets oxidized, or maybe you look at your knickers in another light, so to speak, when you take them off the line.