This is incorrect too. Beauregard sent a message to Major Anderson informing him of the arrival of Lincolns fleet of belligerent warships. He asked Anderson for a truce. He informed Anderson that if Anderson would not fire on his men, he would not fire on Anderson.
Anderson responded that if Beauregard fired at any ship bearing an American flag, Anderson would use all the guns of Ft. Sumter to attack him.
So it looks like Anderson was the one who actually sent an ultimatum.
In fact, Confederates had many times demanded Fort Sumter's surrender, going back to December 1860.
Maj. Anderson, Presidents Buchanan and Lincoln had always refused.
By April 1861 there was nothing conditional or "truce" about Confederate demands -- on April 11 & 12 they again demanded immediate surrender and when Maj. Anderson tried to delay, Jefferson Davis' orders were that Fort Sumter be "reduced".
The Confederates' final order to assault Fort Sumter came when only one Union ship, the Revenue Cutter Harriet Lane, sat out of sight, well outside Charleston Harbor.