It is important to remember that the same action can be described in different ways (tenses & aspects) so it is NOT the action that determines the tense but the image that the speaker wants to communicate about the action. Here we have the speaker describing finished TIME, so a PAST TENSE makes sense. Now which ASPECT between CONTINUOUS and SIMPLE? The Continuous or Progressive describes an action like a VIDEO, something we imagine 'happening', (or temporary or changing) The Simple aspect describes it 'simply'. As an event, a fact, permanent - something that cannot be interrupted - like a PHOTO. So here do you want the listener to imagine a singular fact "He shouted at me" or a continuing action "He was shouting at me" - I think with the "ALL DAY" the speaker wants to emphasize an ongoing action, so the Past Continuous would communicate the image the speaker would like us to imagine. Note how 'all day' could be used with the Past Simple, for example: Why did he stay here all day? Here the speaker is interested in why the event (Simple) happened, not why the action (Continuous) was happening.

Why did the manager shout all day yesterday? Simple past. The action is finished plus you have the word "yesterday" which places the action in the past. Why has the manager shouted all day? "All day" present perfect, started in the morning, for example, and still going on.

Why was the manager shouting all day yesterday?

It's better to use the past progressive here to emphasize that the action was performed continuously in the past. The present progressive is used similarly to talk about an action that someone is constantly doing. "My friend is always texting on his phone." It makes it feel like every time you see your friend, he is in the middle of texting someone.