The trip to the Tines' world was not itself part of the humans' plan.
We see this passage when they're looking over the planet:
It was certainly not intended in the original escape plans. They were to meet with the High Lab’s frigate—and all the adults who could escape from the High Lab. And of course, that rendezvous was to be in space, an easy transfer. But the frigate was gone now, and they were on their own.
Later, the Skroderider confirms:
They did not prevent it, but they did plan to escape the laboratory planet with two starships. And they did get word of their attempt into channels that ended with my acquaintance at the beach party. And here is the important part. At least one of these ships was to carry away some final elements of the Perversion’s recipe—before they were incorporated into the design.”
“If this is true, then the Straumers may have a chance. It all depends on the missing parts of the design document.”
“Just so. And of course the humans realized this too. They planned to head straight for the Bottom of the Beyond, rendezvous there with their accomplices from Straum.”
Shortly after that first quote, we see this:
“All this for nothing!” he said softly. “We made a monster, and ran, and now we’re lost at the Bottom.” And Mom’s voice even softer: “For the thousandth time, Arne, not for nothing. We have the kids.” She waved at the roughness that spread across the wall. “And given the dreams…the directions we had…I think this was the best we could hope for. Somehow we are carrying the answer to all the evil we started.”
Which suggests that the countermeasure (or the digital ghosts of the researchers who were partly caught up in the rapid intelligence uplift of the automaton) had given the plans some prompting and instruction through dreams or more direct directions. To some extent, this probably dictated their course towards the edge of the Slowness, but probably not to the specific planet.
Given that the end of the book
has the countermeasure construct an incomprehensible machine that taps the power of a local sun to alter the zone boundaries on a massive scale and encyst the Blight.
It's reasonable to assume that it might require being near the zone boundary to properly function, although I don't believe we ever get it spelled out.
The closest I can find is this:
A thousand light-years? Ten thousand? I’m not sure. The ghosts in Countermeasure—Arne and Sjana thought it might rise so high it would punch into the Transcend, encyst the Blight right where it sits…. That must be what happened Before.”
Which suggests that the general location (bottom of the Beyond and a position where a successful operation would swallow up the threat) might have been deliberate.
However, the trip towards the Slow Zone doesn't necessarily need any transcendental planning at all. For a threat such as the Blight, this seems like a fairly obvious approach to anyone aware of basic zone properties.
The Skroderiders talk about how getting lower in the Beyond is safer when dealing with threats on this scale:
“True, simple caution can prevent many disasters. And if your lab is in the Middle or Low Beyond, such caution is all that is really needed—no matter how sophisticated the threat. But we all understand the nature of the Zones….”
and Ravna in the same conversation thinking:
Most likely both ships had been destroyed by now. If not—well, the Straumers had been at least half-smart, heading for the Bottom.
And later Pham Nuwen:
The whole basis of the Perversion—thermodynamic, economic, however you want to picture it—is the high quality of thought and communication at the Top of the Beyond. The Perversion hasn’t touched a single civilization in the Middle Beyond. Down here, the comm lags and expense are too great, and even the best equipment is mindless. To run things here you’d need standing navies, secret police, clumsy transceivers—it would be almost as awkward as any other Beyonder empire, and of no profit to a Power
So, if you're facing a newly transcendent Perversion that might want you dead or controlled (either because you're carrying the secret to its destruction or just because you can warn people), fleeing for the part of the galaxy where its powers are at the weakest and yet you can still operate FTL stuff, that is, just near the border between the Slow Zone and the Beyond, seems like the most logical place to go, at least as a first step before you come up with something better.
Landing on the Tines planet, though, that seems to have not been intended (or if it was, the planning was far too powerful and subtle for the human minds we see most of the story through to even be aware of).