That's called Vasovagal Syncope [0]. It doesn't necessarily happen because you see your own blood in a bag, but rather because of the physical implications of having blood removed from your body. Drawing slower or smaller volumes can potentially help mitigating this problem. I think it can also be seen as an indicator for other medical problems regarding your circulatory system, so it might be worth investigating further.

0: https://en.wikipedia.org/wiki/Vasovagal_syncope