My explanation is that evasion moves’ turns are counted based on your opponent’s dinos’ actions. Basically the same way Shields work.
For example if you use Shielding Strike/Deliberate Prowl against a faster opponent, after your opponent has used their turn, the shield/evasion will lasts until after your opponent makes their next move.
You could argue that the shield/evasion isn’t actually waiting for your opponent to make their next move, but for your own dino to make it’s next move, but that can easily be proven false: use a Shielding Strike against a slower creature, after you’ve been slowed by Superiority Strike.
My recommendation is to use it in Campaign under the “Fierce creatures” section (facing opponents of defensive disposition). There’s a stage where you face an Apatosaurus and Parasaurolophus, and Para is perfect for this, since it goes SS-Impact and run, meaning the order will go: you use Shielding Strike, opponent uses SS, opponent uses Impact-and-run, you use Shielding Strike, then you use some other move, but the shield still stays until Para/Apato hits it.
In the OP’s scenario, because Strike-and-run was used, you’ve already been hit once, counting as 1 turn, then SI-Savagery hits again, counting as a second turn. You might say that hit-and-run run moves are overpowered for allowing the opponent to get 2 turns, if the next creature has an SIA, but you’d have to take that up with Ludia. That has always been the point of hit-and-run moves anyway. It’s intended.
Like I said, it’s debatable that Ludia should word some of the move descriptions better, and the word “turn” could be replaced by “action” or “move” in some places, but Ludia has never responded to these queries.
In case you’re curious, there is evidence suggesting all SIAs are counted as separate turns anyway. We’ve discussed this before on the other threads.