I agree with Obsidian that it wasn't dispersed properly.
I've never use zinc oxide to whiten/lighten my soap, but I do use titanium dioxide, which works great for me. I normally use anywhere from 1/2 US teaspoon to 1 US teaspoon of TD ppo, depending on what other discoloring additives I might be using, such as certain FOs, etc.... I don't like to go over 1 teaspoon ppo because I get chalky-feeling soap when I do more than that.
How white or light of a soap TD gives you depends on your oils/fats and the discoloring power of your additives. Some additives, such as FO's with a high % of vanillin in them, for example, aren't affected by TD very much and you'll end up with a dark soap, regardless. I've never used tea infused water, so I cannot say how light or dark of a soap one will end up with if using TD.
I mix my TD with enough vegetable glycerin to make a somewhat thick, but smooth slurry. To get out any lumps, I like to mix it with
this mini-mixer made by Badger . Then I add the smooth slurry to my soap batter and use my stickblender to make sure it's dispersed well in the batter before pouring into my mold. I never get any of those pesky white dots when done this way.
IrishLass