Since this ability specifies "next" and "this turn," adding "UEOT" would be redundant and unnecessary, correct?

You are correct. The wording is fine in that regard.

What's a "color type", though?

Also in your graveyard you'll find a "creature card" rather than a "creature". For similar reason you'll refer to "exiled card" over "exiled creature".

Usually this effec would probably be realized as "Add , Spend this mana only on" etc. I'm not certain how relevant the cost reduction over multiple phases is to the design.

I think I tinkered with using creature type over color and didn't delete the original text. "Add . Spend this mana only to cast a spell that shares a color with the exiled creature card." just doesn't look as visually good as a chunk of text, but I suppose it's more standard then it must be so. At that point, I guess it could make colored mana, since generation looks janky next to a specific color requirement.