Perhaps you are forgetting that Lincoln's armed expedition started arriving off the Charleston bar before or about the time that the ultimatum was delivered to Anderson to surrender the fort. If Anderson could hold out for a couple of more days like he asked for, the whole expedition might have arrived and saved him from surrendering and/or aided in his fight with the Confederates like the New York Times article I linked to above had forecast. I think that is why Anderson asked for the extra two days.
The South knew the expedition was coming, first from leaks from Northern friends, Northern newspaper articles saying something was up and that ships were heading south, and finally a messenger from Lincoln gave a note to the Governor shortly before when the expedition was supposed to arrive. Should the South have waited for two more days for Anderson's allies to arrive so that Anderson could better resist the demand to surrender?
Unfortunately for Lincoln's Sumter expedition, a storm at sea had delayed the expedition and separated its ships. The tugs that were supposed to take supplies in to the fort never made it through the storm. Once all the expedition's ships other than the tugs had arrived (not counting the Powhatan that Lincoln had diverted to Fort Pickens without telling the expedition), the attack on the fort was already underway. And critically, the seas were too rough for them to make it over the Charleston bar to join in the fight. The weather gods had voted in favor of the South.
I'm gone for the rest of the day.
Not forgetting it. Davis chose war, he fired on a Federal fort, and issued letter of marque to raid federal shipping. Both recognized acts of war in international law.