The Thrintun stasis fields were generated from inside the field.
You see that un-shiny bump on the back? It sticks out of the field, just a little. Just a few molecules. I think it was the switch to turn off the field. (World of Ptaavs)
The stasis field works by retarding the flow of time within the field:
We developed a field that will make six hours of outer, normal time equivalent to one second of time inside the field. [...] I believe the statue is an alien being in a time-retarder field.
Kzanol (World of Ptaavs) estimated that he had been in stasis for about two billion years, that's about 63 quadrillion seconds. There was no indication that any noticeable amount of time passed for him inside the field, so let's say no more than a tenth of a second, meaning the ratio might be "only" 630 quadrillion to 1.
Assuming that the mechanism for collapsing the field doesn't involve any faster-than-light signalling, it would therefore need to be confined within a few nanometers of the surface of the field in order for the button to be able to work quickly. That's plausible, and there's no real reason why the rescue button would need to work quickly anyway; if it takes a few hours or even a few years for the field to drop after the button is pushed, so what? Given the level of technology required to create a stasis field in the first place, this could work.
Another possibility is that the field can be collapsed from the outside and the rescue button contained an external mechanism to do exactly that, rather than being attached to a mechanism inside the field. In fact, we know the field can be collapsed from the outside, because that's how Kzanol was eventually released. I don't think this is what the author intended, and there are issues (what would it use as a power source?) but it can't be entirely ruled out from the minimal information we have.
The Lying Bastard's stasis fields were probably also generated from the inside, but might have been controlled from the outside.
"Our engineers have coated the hull's inner surface with a transparent conductor. When the airlock is closed and the aperture for the wiring conductor is sealed, the interior is an unbroken conducting surface."
"Stasis field," Louis guessed.
"Exactly. If danger threatens, the entire life-support system goes into Slaver-type stasis for a period of several seconds."
The stasis fields continued to work even after the rest of the ship was destroyed:
"The wing's gone."
So it was. So was everything that had been attached to the wing [...] The hull had been polished clean.
That strongly suggests that the field generator was inside the field, because otherwise it would have been destroyed at this point; we know that it wasn't because the stasis field was used again a few pages later.
However, it is possible that the mechanism for triggering the collapse of the field was on the outside; we'd already concluded that it had to be very small, possibly only a few nanometers thin, so it could perhaps have been fitted between the conductor and the hull, along with enough computing power to decide when the field should be collapsed.
On the other hand, the description of the Lying Bastard's defensive mechanism suggested that the stasis fields went on for only a few seconds at a time, presumably the length of confinement being determined when the field was activated. If the situation is still dangerous, the stasis field could be immediately regenerated, too quickly for the crew to perceive it. (This is similar to the mechanism used in Marooned in Real Time by Vernor Vinge, already mentioned by Zeiss Ikon in the comments to his answer.)
In short, we don't have enough information to be sure how these things are achieved. But taken in context, and given a modest dose of suspension of disbelief, they do appear to be plausible.