Well, yeah, definitely the recap is off. A lot of things actually happened!
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She starts off with Blade Rush, while you’re not facing her. She obviously had the helix skill that makes blade rush explodes on contact, meaning the small shield damage you take at the very beginning was due to the AOE component of the skill. It appears in the recap, by the way. Since it’s marked as “slow”, I’m guessing that means the SKILL itself was slow ( a consequence of the AOE helix modification on the skill ).
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She TPs on you. This deals damage but she seems to miss you… However this may kick in her shield recharge if she had taken the helix modification, meaning an extra layer of protection against the turrets ( which rarely shred anyone really, even early game, so you can pursue someone, kill him, and still go back to safety with almost any character in my experience - especially against slow-ass rockets turrets !)
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The ult, well, something I hadn’t thought of yet : I think she initiated the ult before teleporting behind you, meaning the animation ended when she was ALREADY behind you, resulting in you believing she insta-casted it. There is a delay before the blades fall that she took advantage of…
But this is actually the big part that indeed isn’t shown on the recap.
Mathematically, her ult deals 167 damage per second for 5 seconds, and she has at least one activated piece of gear that boosts skill damage, meaning it could very well already be 200/s. Judging from your health, it seems like you took 3 ticks, the third one being the killing blow, with intwined regular attacks that she seems to almost completely miss.
Basically, I’d say you took the recap’ed ~100 from blade rush AOE, 3x~200 from her ult ( NOT SHOWN IN RECAP ! ) and the expected ~90 from regular attacks.
Either that, or you didn’t get the full recap on her regular attacks. She may have True Striked you ( right mouse button attack, sensibly higher damage than regular left click ) and you only got hit by 2 ticks of her ult… But I’d tend to think only the ult didn’t show up on the recap and everything else was right.
At any rate, while this was brutal it seems legit - but I fully agree that the recap was nigh useless for you to understand what could have happened… 

). They are still possible, but it’s not possible to track them with the recap. Basically, stop hurting yourself for now and stop using that square button when you die.