There are actually two chemical reactions going on at the same time when you combine the solutions. During these reactions two forms of iodine created – the elemental form and the ion form.
In Reaction # 1 iodide ions react with hydrogen peroxide to produce iodine element which is blue in the presence of starch. BUT, before that can actually happen, the Vitamin C quickly reacts and consumes the elemental iodine.
The net result, at least for part of the time is that the solution remains colorless with excess of iodide ions being present. Now after a short time as the reactions keep proceeding in this fashion, the Vitamin C gets gradually used up. Once the Vitamin C is used up, the solution turns blue, because now the iodine element and starch are present.