I think the artcle might be missing one core premise of ACT - that it is not meant to help you to deal with negative emotions it the moment all that much.

The book on ACT I'm reading (happiness trap - from the founder of the technique) goes to great length to say that trying to "deal with negative emotions" (anxiety, sadness, etc) using affirmations, rationalization, etc is a dead end - it's not helping in the long run most of the time and is actively distracting and takes a lot of effort that could be put elsewhere.

The suggested path (that i am finding somewhat helpful) is to learn to act in accordance with your values regardless of how you feel and the story you tell in your head. It will still suck balls day to day, but on top of that, in the long run, you will feel more at peace and in control and respect yourself for following your chosen path.

The core realization is that while it may seem like your feelings (anxiety) and the story that plays in your head* is what makes up YOU, you may treat these as biological and early developmental "warnings" that your brain has learned to warn you of danger, and you most likely will feel this way for the rest of your life and won't have control over that, but you are actually FREE to choose how to act in response to these situations.

It may seem like these feelings and thoughts are making you act in a certain way, but they are not!

In your example, the feeling of financial anxiety could be accompanied by a thought like - "shit, how am i going to pay for that, why does it always happen to me, how do i fix it, why do i have to ruin it for myself and people i care about by being so sloppy, why does the universe makes it so hard for me and so much easier for others.." - and there's nothing you can do to change that feeling or that thought pattern in your head.

But what you can do is to use one of the techniques to (very temporarily) tune out of this thought train, check in with your values (eg taking care of loved ones), and choose a course of action that fits these as much as possible given the circumstances (eg find a way to spend quality time with them on a tighther budget) and DESPITE all that noise in your head.

A large chunk of the book is focused on consciously discovering your core values.

Is it easier to act with integrity (eg not snap at loved ones) moment to moment if you are not under financial stress or if that stress was not a part of your upbringing? Sure as hell! And given these unfair and idiotic and unnecessary circumstances that caused your internal machinery to work the way it does right now (stay alert at all times), it is your decision to commit to a further course of action - either numb your pain short-term (by ruminating, or alcohol, etc) or act in accordance with your values. Your (highly uncooperative ancient meat lizard) brain will still pull you towards a short term fix - because it is its primitive reward-seeking job, and you will inevitably loose control and let it win sometimes (esp under stress), but there is a part of you that can choose to patiently course correct your behavior towards your higher level values every time that happens. Or maybe you know that at this very moment you do not have resources to course correct much - and that's okay, as long as you are being honest with yourself and act accordingly (eg "i need to find a way to take better care of myself atm - to free up resources to take better care of others, it would be against my values to overwork myself to the bone and be so exhausted that i struggle to catch myself when I'm being mean to them").

One additional realization that i found helpful is that, in the face of such challenges, your brain is quite good at making you think that it knows how everything works - so you feel more in control, and so that the path of least resistance (doing nothing or numb your pain now) seems like the most rational one that agrees with your values. An antidote to that I found helpful is to remind yourself that you know very little about who you are (beyond the silly story playing in your head on repeat), and how you will react to things, and who other people are, and what's going on for them. So you can choose to plan your behavior to align with your values under the assumption that you know infinitely little about both yourself and others.

tldr is that pain is inevitable, but you may reduce (but not eliminate) suffering if you learn to act with integrity in the face of it