Sallatha Sutta and modern psychology
I think they're related but not identical.
I think the Sallatha Sutta can be paraphrased along the lines of, &quot;physical sensations lead to feelings (I feel that I like this, or that I don't like this) which lead to attachment (I want this to continue, or I want this to stop)&quot; -- which means that, now you have two problems, i.e.

an unpleasant physical sensation
not getting what you want.

That's what's meant by,

&quot;... So he feels two pains, physical &amp; mental&quot;.

I think the reason given for the second pain is,

... he is resistant. Any resistance-obsession with regard to that painful feeling obsesses him.

So I think this is an example of clinging or attachment causing suffering.

He does not discern, as it actually is present, the origination, passing away, allure, drawback, or escape from that feeling.

Instead he ought to see that the feeling (and sense-contact) is impermanent, that it arises and passes away, and not be attached to it.

Whereas a disidentification or decentering which you quote from the 2002 paper by Teasdale seems to me, not exactly the concept of 'detachment' or of seeing impermanence, but more specifically the concept of 'anatta' or 'non-self'.
For example, the article &quot;No-self or Not-self?&quot; suggests that any concept of self is a cause of suffering.
There's a description of decentering in the Gaddula Sutta,

It's just as when a dog is tied by a leash to a post or stake: If it walks, it walks right around that post or stake. If it stands, it stands right next to that post or stake. If it sits, it sits right next to that post or stake. If it lies down, it lies down right next to that post or stake.
&quot;In the same way, an uninstructed run-of-the-mill person regards form as: 'This is mine, this is my self, this is what I am.' He regards feeling... perception... fabrications... consciousness as: 'This is mine, this is my self, this is what I am.' If he walks, he walks right around these five clinging-aggregates. If he stands, he stands right next to these five clinging-aggregates. If he sits, he sits right next to these five clinging-aggregates. If he lies down, he lies down right next to these five clinging-aggregates. Thus one should reflect on one's mind with every moment: 'For a long time has this mind been defiled by passion, aversion, &amp; delusion.' From the defilement of the mind are beings defiled. From the purification of the mind are beings purified.

I think there are two related concepts:

Detachment from the clinging-aggregates (perhaps by observing arising-and-passing-away, which is an object of vipassana meditation)
Learning to avoid the view that, &quot;This is mine, this is my self, this is what I am&quot;.