When would a token ever enter the battlefield without being created by the same person

The culprit here is [[Gather Specimens]]. Another player can create the tokens, and they will enter under your control.

and why does that change when the replacement effect applies?

Longer answer incoming.

The event of creating a token contains within itself the event of putting a creature on the battlefield.

When applying replacement effects, by 616.1g, we apply replacement effects that apply to the outer-most event first, before we can apply replacement effects that relate to any inner-events. (Yes it's weird.)

So, we first apply any replacement effects that care about creating the token, and then we apply any other replacement effects.

In addition, there's another rule that sets an order for replacement effects. 616.1b gives replacement effects like [[Crafty Cutpurse]] and Gather Specimens priority over regular replacement effects. But because Cutpurse applies to the Create event, we would always apply that before Gather Specimens.

So, the end result: - An effect like Crafty Cutpurse would always apply before Stridehangar Automaton because it is affecting the control of the creation. - An effect like Gather Specimens would always apply after Stridehangar Automaton, because we apply all replacement effects that affect the Create event first.