I want to describe the event of eating pizza, which took place in the past, looking at it back from the present.

In case we use the adverbs {pIj}/{roD}, then (if my understanding is correct) we need to write:

pIj pItSa' vISoppu'
I've often eaten pizza
(here the aspect {-pu'} is used)

roD pItSa' vISop
Customarily/habitually/regularly I've eaten pizza
(here the aspect {-pu'} isn't used)

Whether or not -pu' is used doesn't depend on the meaning of the adverbial, but on the meaning of the sentence. If you're describing specific instances of actions, use -pu'. If you're describing habits or tendencies without specific instances, don't use -pu'.

In English, the difference might be expressed thus:

During the previous summer, I often ate pizza. (You're describing specific instances of pizza-eating, so this is perfective.)

During the previous summer, I would often eat pizza. (You're describing a tendency to eat pizza. That would is the key to recognizing the imperfective nature of the idea.)

Now, suppose we want to say "in the past, sometimes/occasionally I've eaten pizza", and we're looking back on the event. Do we need to use the {-pu'} here?

Same consideration. Are you describing the eating of pizza or the tendency to eat pizza? It's not about the adverbial; it's about what you're describing.

-- 
SuStel
http://trimboli.name