With a different ruling's clarification that an action's resolving is a full stretch of time and not a point in time, I've taken the liberty of clarifying the CR Glossary entry under Additional actions.
An additional action granted by an action of the same designator (Battle granted by a Battle and so on) is delayed until after the current action resolves (clarified from "until it resolves").
By the timing rules, delayed effects triggered by a point in time come before Reactions to that point in time. Therefore, for now, Reactions triggered after an action resolves (such as Cut Them Off) will come after any additional action is taken. This is the least radical change possible without a major announcement, but after GenCon the Rules Team will be reviewing the timing of additional actions.