He will only apply anti-magic after the mage's turn)) Now, think about what the mage can do in one turn? ... If it's hypnosis, then who will move after the mage? Not the mantis, right? )
Any summoned creature starts moving immediately after it is summoned. The druid makes Anti-Magic on himself on his first turn. It doesn't matter what the mage will do. Druid's turn - summon the mantis. Mantis's turn - flies to the mage (even if it doesn't deal damage). The mage casts hypnosis on the mantis. The druid casts anti-magic on the mantis, and the hypnosis effect disappears. And now it doesn't matter what the mage will do. With his turns, the druid will summon mantises. The mage becomes useless on the battlefield.