Hello, I am a second year chemistry undergrad. The pneumonic you need to remember is OILRIG; Oxidation is losing, Reduction is gaining. You then need to identify what is gaining/losing an electron. Caesium starts off neutral, then forms
Cs + in the salt, CsBr. Caesium has lost an electron and therefore is oxidised. Bromine has gone from being neutral to being negatively charged, it has gained an electron and so is reduced.
An oxidising agent oxidises what it is being reacted with and so the oxidising agent is reduced. I think you understand that concept, you have just got your answer muddled! I hope this helps!