Well, I think there are many possible answers to this. Interpretation of both the Torah and the Talmud is called midrash -- from lidrosh, "to seek" -- for a reason.
But what you're pointing to is clearly the point of the story. Yes, it was unambiguously a voice from heaven, i.e. God's voice (or perhaps an angel speaking on behalf of God, or some part of God's not-always-entirely-unitary-or-simple selfness). That's the whole point of the story. The sages overrule God. In fact the point of the story, teleologically speaking, is to establish that the sages can overrule God.
Did they feel weird doing so? I don't know; I expect they felt stubborn, and pissed off at Eleazar for showboating, and pissed off at God for intervening, and possibly scared. But they definitely felt that they were in the right to do so, and a good thing, too, from my perspective.
Here are some clues that help answer your questions. Consider the Prophet Elijah's report of God's reaction: He laughed [with joy], he replied, saying, "My sons have defeated Me, My sons have defeated Me."
Did He laugh "with joy"? That's in brackets, so some commentator added that. Perhaps He laughed ruefully, or perhaps He actually found it hilarious. In any event, He was clearly surprised -- surprise is an element of laughter. He clearly saw it as a kind of competition -- the sages "defeated" Him. And He clearly was delighted -- or at least grudgingly amused -- to have lost. And for me, the reason is obvious from the word "sons". Because that's precisely the relationship in which you'd feel competitive, you'd try to intervene and control things, and then when you fail, when you are defeated, your reaction would be pride. I remember when Aviva started smoking me at poker, and when Knees Tag became unplayable because the kids got too good. I was so excited.
The other clue is Gamaliel's appeal which stops the tsunami: "Sovereign of the Universe! Thou knowest full well that I have not acted for my honour, nor for the honour of my paternal house, but for Thine, so that strife may not multiply in Israel! "
Consider: he's about to get whacked by a tsunami. He says this and the tsunami is calmed. The effect of his words is clearly to change God's mind. Is this because he provides new information? No -- as he says, "thou knowest full well". So why does it change God's mind? Presumably because he's calling God to account, reminding Him of his responsibilities and the consequences of His actions. That's why my gloss on it is: "Yes, yes, I got it, I voted down Your Heavenly Voice. But do you think Eliezar is the only one who can call down Your Heavenly Voice? Let's face it; you're kind of a loose cannon here."
The God of the Tanakh really is a loose cannon, constantly flipping out and destroying nations and species, then regretting it. The God of the Talmud seems mellower by comparison, but still not necessarily the most consistent dude.
In your analogy, they blow off the boss, or rather they say "hey! that's not your department, all right? you delegated that!" ("not in heaven!") and then later the boss is mad and calls the tech lead into his office in a tsunami-mood, and the tech lead calmly says, look, this isn't going to work out for you to delegate decisions and then meddle. I did this for your sake. And the boss says, ok, ok, I get it.