Anderson had no desire to start a war. His occupation of Ft. Sumter seems to have been based on a desire to safeguard his force while gaining time for the politicians to work out the situation. OTOH, he was a very good professional officer who would have done his best to carry out any instructions he received from his superiors.Taking the offensive, turning the secession crisis into a shooting war, would be a profound political decision, not for Major Anderson to make. AFAIK he was a responsible officer, not given to recklessness or exceeding (violating?) his orders.
As @WJC said, the Carolina/Confederate troops were not very experienced either, but two green forces fumbling in the dark has potential for disaster.
The point here might be that it is Winfield Scott sitting at the top of the Army and advising Buchanan. Scott had a long record, including diplomatic successes. He was a hero in the War of 1812 and in the Mexican War. Andrew Jackson had put him in charge of operations in Charleston during the Nullification Crisis, so Scott's ideas would be based on real experience along the South Carolina coast and in Charleston harbor.
I would guess that Scott would not want a shooting war in Charleston to start either. His idea was probably to strengthen Anderson as a negotiating point, a show of strength to prevent the loss of Federal positions rather than an offensive move. He had negotiated the US out of potential shooting wars with Britain twice, the last time when George Pickett almost started the Pig War with Britain on the Pacific coast. Most likely, Scott wanted to settle this mess without shooting and he would have trusted Anderson (who he regarded as a man on the same level as Robert E. Lee) to do as he instructed.