A reaction is an instant response to a trigger of some kind, which can occur on your turn or on someone else's. In typical game mechanics, a round is 6 seconds and turns occur nearly simultaneously within that time. A reaction is 1 second.
Reaction spells are very quick to cast:
Some spells can be cast as reactions. These spells take a fraction of a second to bring about and are cast in response to some event. If a spell can be cast as a reaction, the spell description tells you exactly when you can do so. roll20 compendium
Since neither this nor the spell descriptions state that you must be holding the material components, you do not need to be holding them when the trigger occurs, but they need to be readily accessible. For example your components pouch hanging on your belt, not in your backpack. In most cases, the components pouch functions the same as a spell casting focus. See this question and answer: What is the difference between an Arcane Focus and a Component Pouch?
Looking at the counterpoint:
If you required that the material component had to be held at the time of the triggering event, you'd be forcing the character to choose which spell he can cast because he could only hold one material component at a time. Well, two if he used both hands. This does not seem to be the intent of reaction spells since they are already limited by the triggering event.