I agree a "sugar fit" is probably what is more often called a "sugar rush" - feeling too energetic like you ate a lot of sugar.
"Put that on 'em" could mean a lot of things. Without context it's too vague to really mean anything. In the context of her song though, "that" is probably a "spell". She's talking about seducing men, and it's not uncommon to talk about love like it's a magic spell.