I want to agree with your position. I've seen some data about suicide rates based on parenting strictness, and have anecdata of losing people due to exactly this style of parenting. The tradeoffs some parents make when faced with extreme poverty are sad. Hell, the fact that a modern industrialized society has as many suffering people as ours does is sad.
But I don't think your refutations hold up. This will be a bit of a tome, sorry.
> For those [parents] that are absolutely poor and barely surviving they have little time nor energy to actively participate in their kid's schooling.
That's true for a lot of people. Structural disadvantages are huge. But at the same time, it's not true for large classes of deeply impoverished people. As the author of TFA pointed out, [east] Asian immigrants are, by some metrics, the poorest group of people in the New York area--and definitely severely economically disadvantaged no matter what measurement you use. And yet the academic performance of those groups--even in that area--continues to surpass many others. Given how endemic poverty is among those demographics, I don't think "it's not the poor kids doing super well in school" holds up; the intersection must be large, and something must be materially different about the practices of those folks in order to combat what, elsewhere in the country/world, would be the multiple-generation-damning sentence of poverty.
> Families don't pull themselves out of poverty through adherence to education or work ethic.
That's anecdotal. In general, this is a dangerously politicized area. To argue that families do not, as a rule, pull themselves out of poverty flies in the face of many areas in which they do so in very significant numbers (like the one discussed in the article). However, to argue that therefore all impoverished families can and/or should do this is to echo the most callous and ignorant positions of modern American conservatism.
I think that escaping poverty is possible--not just among outlier families out in the statistical noise--and that figuring out how/when this occurs is important to improving a lot of people's quality of life. I also think it's super important not to let those investigations ever take on the tone of "...and anyone who doesn't bootstrap themselves out of poverty has nobody to blame but themselves". Study in this area must not come at a tradeoff with acting compassionately--compassionately at macro (e.g. political/voting and economic policies/investments), medium (e.g. donating to causes and activism), and micro (e.g. offering what help you can to people you see suffering on the way to work each day) levels--towards those struggling with poverty.
> there's also survivorship bias in play.
I can relate to this personally, having lost people (suicide, overdose, other) due to circumstances correlated with both insanely strict parenting and severe poverty. But I don't think these answers to the question of "how/why/when do families escape poverty with minimal outside assistance?" is an instance of survivorship bias. The hypothesis being tested is "X allowed these specific groups to escape extreme poverty". Nobody's arguing that many (most) others in that situation don't escape, and nobody's arguing that poverty doesn't exist because some people escaped it--that would be survivorship bias. As you point out, there may be long-term costs that are being overlooked, but that's not the same thing.
When you say "On average those exposed to this style tend to do worse", do you mean worse compared to remaining in poverty? If so, citation needed. Or do you mean that "tiger" parenting has worse outcomes compared to other strategies? I don't think most people would disagree with you there. The important question, though, is why this strategy is practiced so effectively among severely impoverished people, and why it has positive results compared to the "control" majority--which, as you point out, is a vicious cycle of poverty feeding back into lack of energy feeding back into lower parent participating feeding back into stunted academic development.