Why usage of た and not ている in the following usage

Question

I was watching a Japanese Drama, and I have questions regarding the usage of Past tense (た) instead of Present Perfect (ている) in the following sentence.

In this Drama a person was looking for someone and as soon as he finds him (both are present in the frame and he just finds him) he says, 見つけた (I found him), rather than ている as in 見つけている (I have found him).

As per my understanding of the following articles on the Stackexchange, ている is used to show both Continuous Aspect and Present Perfect (More or less dependent upon whether the Verb is Punctual or Durative). When some fact of the past is related and is being talked about in relation to present Present perfect is used as per @Naruto san. Example 知る is used as 知っている, even though we have learned (known) about him in the past, however we use ている as the focus is not on the fact that we learnt it in the past but on the fact that whether we know someone or not i.e. present.

Likewise, why was not ている used in 見つける. As in this case as well, even though as soon as he found him the action was complete and it changed to past. However, the focus is on the present i.e. the fact that he found him, and not of that he found him in past, but just on the fact that he found him. So, in this case, as per my understanding of the following resources. 見つけている should have been used.

Question:

1. Is my understanding correct?
2. Should 見つけている be used instead of 見つけた, given the facts of the scene of the drama?

Resources used to gather this understanding:

a. When is Vている the continuation of action and when is it the continuation of state?

b. Usage of ている in Punctual Verbs in Japanese and the Concept of Present Perfect in English

c. Is 寝る a stative or active verb?

d. If Vて+いる isn't a gerund, then what is it?

Answer 1

I believe generally in Japanese immediately upon completing a task, you use the past tense.

Examples range from

• やった
• できた
• 出来上がった (said almost immediately after preparing a meal to essentially say “dinner’s ready.)
• みつかった

Perhaps if a fair amount of time has elapsed (like a day or an entire week—I suppose “fair amount of time” would depend on the urgency of the situation), it might make sense to say 見つけている. (An urgent situation might be a parent with Alzheimers who walked out of the house and no one know where they are.) But immediately after the accomplishing something, no.

Answer 2

ている implies an ongoing action.

In English, you don't say "I'm finding someone", you say "I'm looking for someone". To "find something" means the action of looking for something is finished. The object is already found.

Likewise, in Japanese you say "友達を探している", not "友達を見つけている".