Citation please.
There is an interesting assessment of Gillmore's actions that reaches an opposite conclusion. See: Article on page 37 by Christopher A. Mekow. Here are two excerpts:
Taken as a whole, the bombardment campaign in the greater Charleston area would reach an intensity hitherto inconceivable by Confederate defenders and local residents. But was there any military legitimacy for firing on this city, the “Cradle of Secession”? By exploring the basic philosophy of eighteenth- and nineteenth-century warfare, and by then comparing the bombardment of Charleston to the sieges of Vicksburg and Petersburg, this study will assess a policy that arguably ran counter to contemporary military doctrine, namely the shelling of civilians in the absence of clear military objectives.
... Thus, the bombardment of Charleston began that morning of August. Yet the circumstances surrounding this event differed greatly from the sieges of Vicksburg and Petersburg. Unlike the two siege operations discussed earlier, Charleston was not a city besieged, but rather a city suffering an indiscriminate bombardment. British journalist Frank Vizetelli was in Charleston as the bombardment began and wrote the following for the London Illustrated News: "It was now that, foiled at all points, and smarting under his many failures, the Federal general was guilty of that barbarity which has disgraced him as a soldier. Unable to capture the forts in his immediate front, he intimated that unless they were surrendered, he would turn the most powerful guns upon the city."
Gillmore doesn't come off very well in the linked article, in contrast to Grant and even Sherman.
Here is an excerpt from Beauregard's reply to Gillmore following the initiation of shelling the city:
Among nations not barbarous the usages of war prescribe that when a city is about to be attacked timely notice shall be given by the attacking commander, in order that non-combatants may have an opportunity for withdrawing beyond its limits. Generally the time allowed is from one to three days; that is, time for a withdrawal, in good faith, of at least the women and children. You, sir, give only four hours, knowing that your notice, under existing circumstances, could not reach me in less than two hours, and that not less than the same time would be required for an answer to be conveyed from this city to Battery Wagner. With this knowledge, you threaten to open fire on the city, not to oblige its surrender, but to force me to evacuate these works, which, you, assisted by a great naval force, have been attacking in vain for more than forty days.
... It would appear, sir, that despairing of reducing these works, you now resort to the novel measure of turning your guns against the old men, the women and children, and the hospitals of a sleeping city, an act of inexcusable barbarity from your own confessed point of sight, inasmuch as you allege that the complete demolition of Fort Sumter within a few hours by your guns seems to you "a matter of certainty."
Your omission to attach your signature to such a grave paper must show the recklessness of the course upon which you have adventured; while the facts that you knowingly fixed a limit for receiving an answer to your demand which made it almost beyond the possibility of receiving any reply within that time, and that you actually did open fire and throw a number of the most destructive missiles ever used in war into the midst of a city taken unawares, and filled with sleeping women and children, will give you "a bad eminence" in history, even in the history of this war.
By the way, I found some of those Charleston civilian casualties when looking in the Charleston papers of September 1864 for mention of 600 Confederate prisoners placed in front of a Union battery to ward off Confederate fire.
Your earlier mention of inaccurate bombardment at the limit of range reminded me of the indiscriminate bombing of London civilians by buzz bombs.
Many people evacuated the lower part of Charleston that was in range of the Union guns, but the shelling was generally ineffective, so some people continued to occupy areas at the extreme range of the guns. You could argue that by returning or staying in the extreme range of the guns, their deaths were their own fault. But it appears to me to be a clear case of the Union military overstepping the rules of civilized warfare of the time by bombarding civilians without even demanding that the city in question be surrendered. Gillmore wanted the evacuation of forts that were not contiguous to the city or else he would bomb civilians which he did starting in the dead of night.
Okay, you win. Based on your description, it does sound like Gilmore was a jerk.
However, the siege and bombardment went on for months and surely civilians had plenty of opportunity to withdraw.