Buddy... the reason you don't think you need an exterminator is because that exterminator is doing their job successfully every month.

Pest control substances are way more safe than you think they are when used residentially. They mighty not even want to treat your apartment, just check for signs of infestation.

Don't be a dick. What the landlord is asking for is completely legal. Let the exterminator in. And if you are curious about their work, ask them what they're going to do so you're not making assumptions about how their work is gonna give you a third arm.