Prior to 1912 there wasn't any official arangement of the stars in the canton. Anyone producing a flag could do it in whatever arrangement they wanted.

The most common pattern would have been to put them in the common rectangular pattern we're used to today. Other popular patterns would have been to arrange the smaller stars into a single large star, or to arrange them in concentric circles. A particular favorite of mine from the era is the Thirteen/Thirty Four flag which had 21 small stars interspersed with 13 larger stars.

Since around the end of Mexican war, the army had adopted an unofficial tradition of having a diamond shaped pattern used at forts and other permanent installations. But even then the exact "diamond" pattern was up to the local commander. So the Sumter flag would have been representative of what other forts would be flying, but there was variation between forts.