So I was fighting the Vagabond today and I had U.a. Stadium on the field. I was gonna bring back playmaker to Special Summon Slugger on his Amazons but he immediately activated cosmic and banished the field spell. I thought oh I should still get my monster since I activated its effect beforehand but sure enough the vagabond was favored by the duel links deities and I couldn't draw another U.a.
To answer the anon who had a match with amazoness ( not the Op), if you activated before the attack then obviosuly it would work because the trap is removed before the battle even started. If you activated it during attack declaration/ battle step it still works because Cyclone still banishes the card before the actual battle happen (aka damage calc) so yeah.
Continuous Spell/Trap and Field cards must be face-up at resolution to get the effects. If they leave the field you don't get the effect
I noticed Cosmic Cyclone banishes cards and prevents effects
I use it to banish face down Amazon Onslaught to prevent my monsters being banished. It works even when they flip it to activate it