General Tullius is there, he's effectively won the battle. Tullius is portrayed and this amazing general, the best in the Legion. All Tullius had to do was execute Ulfric first ending the war, and I can't see why he didn't. He's the leader and the most dangerous threat to the Empire. The longer he's alive, the more danger the Legion is in. Killing him first would not only effectively end the rebellion but all his soldiers would have known they had lost just before they died.
I guess. I would've done it. Any IRL Evil Overlord should always execute the arch nemesis first and some random men only after that, it says so on the list. 

 But, it seems there was no fear of losing Ulfric, no threat at all that they could think of. The first dragon awake in centuries landing on top of the tower in the middle of the butcher wasn't really a thing they could've thought of beforehand. So maybe they wanted to spare Ulfric for the last, to make HIM see his rebellion and men die before he did. So it's your own logic but the other way round: they wanted Ulfric to know that they've lost, not the soldiers; the whole rebellion personalized so much around Ulfric that making him feel desperate at the scene was the only thing that mattered to the Imperials.
Also, it might've been that the Captain, who clearly was in charge of the situation, was in tremendous pressure, and she didn't think clearly (i.e. sending unwanted men to the block, making not much sense in the order of executing people, etc.) This could've been because the war takes toll on you, or just because Tullius was there yet still she was in charge, or a little bit of these and other factors not mentioned here but possibly present.
 Alduin turns up, and it just happens to be in time to save the (as yet ignorant of the fact) Dovahkiin, the only one capable of defeating him. "No, Meester Bond, I expect you to die escape and spoil my plans for world domination."
Alduin had no way of knowing at that point that one person down there was to become his slayer. He was just casually wreaking havoc near the place he awoke; any place could have done. He was heading there, northeast, for a reason though, to wake up some more dragons on his way.
Also, I don't believe this is a matter of chance. I think the Time-God Akatosh just had pretty good irony going on here with his first-born (Alduin). "Heh, I make sure Alduin flies there just in time to actually save the Dragonborn! :trollface:" Or maybe, just maybe, the player character only "was made" Dragonborn that instant Alduin "saved" him from decapitation, just because he was the closest one to die next. Anyways, the Divines know their irony.