What is the reason for Alexa's reaction?
There are a few reasons, including realisation her friends are dead, understanding their "experiment" with the runner has now worked and possibly terror given the attack she has just suffered at the hands of the machines.
Background to Matriculated:
In Matriculated, a group of human resistance fighters attack and capture a runner. They discuss what to do with it and the following dialogue takes place:
think we ought to reprogram it?"
can't make slaves of them."
"Because that would be simpler."
"We won't beat the machines by making them our slaves. Better to let
them join us by choice."
"But we make them believe their choice is the one we want them to
"Alright, yes, machines are tools that are made to be used. It's their
"…To be slaves."
"That's why we can show them a better world. Why they convert."
"But that world we show them, isn't real."
"It doesn't matter."
"Well, I'm afraid they'll figure out its all in their heads."
"They can't tell the difference. To an artificial mind, all reality is
virtual. How do they know that the real world isn't just another
simulation? How do you?"
"Well, I know I'm not dreaming now, because I know what it's like
being in a dream."
"So dreaming lets you know reality exists?"
"No, just that my mind exists. I don't know about the rest."
So, the key thing here is their desire to convert the runner to their way of thinking, not to enslave it (i.e. to reprogram it).
To do this, they plug the runner (now called "Carl") into a "local" construct (i.e. a Matrix-like world created by the humans). The humans make themselves appear friendly to the runner, whilst making Carl's former body (the runner machinery) appear very menacing. They then save Carl from this machinery.
As this happens, their ship is attacked. They are all brought back to reality and the humans, badly outnumbered are almost all killed. One human, Alexa, is left alive. The runner plugs her, and himself, into the local construct described above, where she soon dies from her injuries, leaving him all alone.
Answering your questions
I think it's vital to explain briefly what Matriculated shows, as it is so vital to understanding your questions:
Why does Alexa react so horrified to the sentinel after jacking in? According to the quote, it is realizing that her crew is gone, and she is trapped within the VR with a robot forever. However her reaction seems for like a feel of terror sourced by the robot itself. As if she is scared of her.
I think there are a few reasons she is to terrified.
Firstly, there is the realisation of where she is - in the simulated reality. Remember the long quote from above. They did not want to make slaves of the runners, but to show them a better world. Remember, "to an artificial mind, all reality is virtual".
The runner wanted to save Alexa, remembered the playful nature of humans in the local construct, and chose to insert her in there, where she (and it) could be happy.
However, Alexa understands the difference between the simulated reality and the actual reality, and realises that inadvertently, despite trying to show the machine a "better world", she has driven it to lock her and itself into the simulated world, believing this reality to be better.
They tried to educate the runner and offer it a choice - and it chose what the humans and Alexa consider to be the wrong option - simulated reality.
Secondly, when she is inserted she is unconscious. She only "awakens" in the simulated reality. When she sees the runner, it is obvious to her that all she knows and loves in reality is gone and she can't go back.
Thirdly, its highly possible that despite trying to convert the runner, after having been attacked (and with all of her friends killed) by the machines, she is feeling resentment and anger. There is only one being that is left alive with her - one of them.
Fourthly, she awakens in agony from her injuries and soon succumbs to them. The extent of her injuries could lead to her horrific look of fear.
I believe it is a combination of these factors that causes her reaction (and rather terrifyingly leaves this newly liberated runner completely alone).
Again, according to the quote, robot foolishly jacks itself into the VR, and the reason to call this act foolish is because they both are trapped in now with nobody to jack them out. However, the robot is seen and the ending scene, by the coast they encountered Alexa for the first time, plugged out.
Foolish is obviously just one interpretation. I've already conveyed my views on why the runner acted in the way it did. The article you refer to suggests it is foolish because it didn't understand Alexa's injuries and thought plugging her in would make things go back to how they'd been before the attack.
The robot is indeed seen and the ending scene seems to suggest it emerged from the simulation, headed to the shore and sat with no understanding of what to do next. This article goes as far to suggest the robot pulls the last coherent image from Alexa's mind, which is what drives it to the shore.