I think they are using the word "presence" here to express the idea of being conscious of being present, being mentally present rather than just physically there but mentally detached. It suggests an engagement or involvement with one's immediate situation, where one is, what one is doing and whom one is with.

"Exerts pressure on achieving 'presence'", to me, means that home technology exerts a pressure that makes it more difficult to feel that you are fully there; it other words, it tends to diminish the intensity of your awareness of being present. Using home technology makes doing things at home more mechanical and you are less involved in the experience; your mind may wander.

There's a good account of this idea of presence in the following passage, from The Oxford Handbook of Virtuality; it speaks of mediated or virtual presence versus consciousness of being present:
https://books.google.es/books?id=viQiAgAAQBAJ&pg=PA589&lpg=P...

I think it is in inverted commas to indicate that this kind of presence is not literal physical presence; the word is being used in a special sense. You can be physically present without having this (sense of) presence

--------------------------------------------------
Note added at 2 hrs (2017-07-15 13:14:14 GMT)
--------------------------------------------------

I think the following sentence in the reference I have cited is relevant to your text: "Presence is the feeling of being in an external world."