https://ffxiv.consolegameswiki.com/wiki/Seasonal_Events

If you're asking what specific Eorzean months these take place, as opposed to real-life months, I do not believe that information is ever provided, in-game or out. In fact, I'm not sure the Eorzean calendar is EVER mentioned in-game, for any purpose, aside from character creation. I can't recall any NPC ever mentioning "the sixth Umbral Moon", or whatever. You'll have to make your best guess. It wouldn't be out of line to use the real-life month to approximate the in-game month, in absence of other data.