Suppose I say: {wa'Hu' jIghungDI', pItSa' vIvunpu'}, for "yesterday, as soon as I was hungry, I ordered a pizza".

Doesn't this give you the impression that my ordering the pizza happened before I was hungry?

I'm asking this because I understand the klingon as "yesterday, as soon as I'm hungry, I have ordered a pizza", meaning that I "feel" it very close to "yesterday, as soon as I'm hungry, I've (already) ordered a pizza".