My first week was/has been quite eventful.

[bruxinha]

I came across the following text last week. It is from a worksheet on mixed sentences and the students have to decide which one fits best in the sentence. Sometimes there are signal words that show you which tense you should use (like yesterday, etc.), but in some of the sentences you have to decide according to the context.
Sorry, I can't provide a real source for this - the worksheet was given to me by a student who got it from his teacher last year. It is somewhere on the internet, not in a book.
The text is much longer, so I'll only write down the parts I need; if some reader needs more context, I can upload the rest. Here are the first sentences:

Mixed Tenses — Restaurant Edition

Task 1: “My first week as a waiter”. Fill in the correct tense form of the verb. Use present, past & future tenses.

My first week working as a waiter at a new Greek restaurant in my city ............. (be) quite eventful. After I ............. (get) the job at the interview, my first day ................. (be) a busy Saturday night.

The answer key is as follows (my bold):
My first week working as a waiter at a new Greek restaurant in my city has been (be) quite eventful. After I had got / gotten (get) the job at the interview, my first day was (be) a busy Saturday night.

I am wondering why the author of the text uses the present perfect in the first sentence. (My student's last teacher gave them the answer key as is and didn't accept other tenses there.) I mean, I can understand the use of present perfect if the speaker is still within this week - let's say, the job started on Saturday and now it's Thursday, so this first week isn't over yet. It has been quite eventful so far (and ist is still going on).
But there is no hint to the time when the speaker is talking about his/her first week. If he/she is already in the second month working there, the "first week" he/she is reporting about is already in the past and fully completed. Would the simple past be acceptable in this case?

 

[jutfrank]

My first week working as a waiter at a new Greek restaurant in my city ............. (be) quite eventful.

This is the opening sentence so there's no preceding context to work with. The natural assumption is that the first week is in past time (the week has ended) rather than future time, so although will be is possible, we're really faced with choosing either the present perfect or the past simple. Both are nice options—the present perfect would be ideal if we were sitting down at the end of the week and looking back at the last seven days, as if we were writing a diary entry. The past simple would present the week as a past event with no present relevance, as if we were narrating the events as more distanced in time. Since we have little idea yet of the nature of the discourse and when it is written in relation to its events, both options are equally appropriate so far. We'll have to read on in order to pick up more clues.

After I ............. (get) the job at the interview, my first day ................. (be) a busy Saturday night.

Okay, now we have more context we can see the text reads more like a past narrative. The simplest solution here is to the past simple in both gaps, but the past perfect is justifiable, though unnecessary, in the first gap. Furthermore, we can now much better justify that the speaker has used the past simple in the first sentence. The present perfect is still appropriate for the first sentence, but the context of the second sentence suggests that the discourse is framed wholly in distanced past time, in which case the past simple is the tense that the speaker would most likely have used.

So all that is to say yes, your sense is right. The past simple is the best tense for all three gaps.