For example:
I ate until I was satisfied (not after being satisfied, but at least it arrived to satisfaction by inference, closed limit on the set.)
I ate before I was satisfied (not arriving at satisfaction, open limit on the set)
She sat until I came back (not after, but up to)
We stop working until our manager says so (work before the event, stop after the event)
He can't accept the invitation until I approve it(before, not up to)

Refactor the sentence. Until triggers the action (looks like it triggers an opposite).

satisfied is the trigger which triggers "stop eating."

"came back" is the trigger which triggers "stop sitting"

manager saying so is the trigger which triggers "start working."

So, when you are satisfied you stop eating.

When you come back, they stop sitting.

When the manger says so, you start working.

Wow, that's a brilliant explanation. Kudos to the logic skills.

However, take this for example:

We can't stop working until our manager says so

      'Until' validates this section                                              
|----------------------------------------|-----------------------------------------|
           We can't stop working         |      We stop working
                                Our manager says so

means the same as

We stop working until our manager says so

                                              'Until' validates this section
|----------------------------------------|-----------------------------------------|
                 We work                 |              We stop working
                                Our manager says so

Disgruntling, isn't it?

We stop working until our manager says so

'Until' validates this section
|----------------------------------------|-----------------------------------------|
We work | We stop working
Our manager says so

Disgruntling, isn't it?

No, that's incorrect.

The manager says not to work until he says to work, is what "We stop working until our manager says so" means.

|----------------------------------------|-----------------------------------------|
We don't work | We work
Our manager says so

So the real question is: does the premise refer to the action or state before the until trigger, or the
event that happen because of the trigger?

According to Tom and Tutorial Doctor, it is the former.

We stop working until our manager says so (work before the event, stop after the event)

So this is valid english? I had no idea, as a non-native english user, this sentence just confuse me...

No, it's not really. "We stop working..." is simple present tense, and "...until our manager says so." wants a continuous tense instead of a simple one. But "stop" doesn't work with continuous tenses. Stopping is defined as something that happens instantaneously. You can't "keep stopping" for some length of time, which is what continuous tense verbs do. If you say "keep stopping" it implies that you stopped repeatedly, not continuously. Whereas "keep going" means continuously, not repeatedly.

Various rephrasings in proper English include:

"We don't work until our manager says to start."

"We stop working when our manager says to [stop]."

"We work until our manager says otherwise."

"We stood idle until our manager told us to start working."

We stop working until our manager says so (work before the event, stop after the event)

So this is valid english? I had no idea, as a non-native english user, this sentence just confuse me...

Hahaha, yes it is. That's incredibly confusing isn't it?
Just try and read many of the books regarding linguistics and English, you will be surprised how inconsistent English really is (not that other languages aren't as well.)

Actually it's not valid English... ^_^;

Ah, I finally see the potential ambiguity. I was parsing the sentence fragment we stop working until our manager says so as having until our manager says so as an adverbial phrase modifying the intransitive verb working, with the word stop as a preposition. The ambiguity comes if the phrase working until our manager says so is parsed as a noun phrase and the object of the transitive verb stop. The latter use is unidiomatic and I would consider it pretty tortured English. It is, however, grammatically valid and the meaning of the word until is still unambiguous, in that it refers to continual action that occurs before an event and has the exact same meaning in both cases.