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I have an Alpha Legion army, and my stratagem reads "Use this stratagem when you can set up an Alpha Legion Infantry unit during deployment. You can set up the unit in concealment instead of placing it on the battlefield. At the beginning of the first battle round but before the first turn begins, the unit emerges from its hiding place - set it up anywhere on the battlefield that is more than 9" away from any enemy models."

The wording in bold leads me to believe that my infiltrators would be set up after knowing who is going first, as it happens at the beginning of the first turn but before it begins. Is this correct?

That is my understanding also.

That is correct. You set up your dudes as the very first thing at the start of the game, after deployment is finished. That's why it's a powerful stratagem.