In setting up a problem or conflict, in a story, the reader will accept "it just happened that way", which means you can handwave away much of the usual "how likely is it?" of the premise. There are magical rings, and hobbits, and that's how it is.
But the main point of a work of fiction is to satisfy the reader, by showing the story coming to an emotionally/intellectually satisfactory ending. Frodo must work and suffer, to finally dump the ring in Mount Doom, god doesn't come down on the penultimate page and helpfully zap it for him.
The term Deus ex machina comes from Ancient Greek tragedies, where, the hero having got into a situation so screwed up he/she can't resolve it, the gods conveniently come down from the sky (in a 'machine'), handwave all the injustices and issues away, solve everything, and hey presto, all nice neat and fairly done.
In modern fiction, that's not seen as a good way to do it. To a reader, it's akin to having read the book, and the last part summarising as "Then the gods came down and solved everything. The end."
('Gods' in a modern context could be any 'plot device', or 'magical' answer that feels like a 'cheat' to the reader, not just a literal god.)
So the comment means that the answer in the story is likely to feel like a "cheat", to someone keenly looking forward to "how will this work out? What will the protagonists do?" And that's why is is being discouraged in your writing.
The thing is, that this often happens at the end, but it doesn't need to. A story sets up its own internal logic, and there is a subtle sense when a new feature or revelation is exposing new internal logic or "reasonable" handwaving, and when it's doing "unreasonable" or cheating handwaving. The latter feels like an author is being lazy and cheating, and can happen anywhere - not just at the end. The more established the plot lines and the more a point sticks out like a sore thumb from its context, the more likely it is to feel that way. Generally after the first 1/4 of a story those have been set up and we are reading about the developing tensions within the universe of the story, so by that point, cheaty solutions and new features have the scope to feel 'cheaty' whereas earlier they may be accepted as part of the setup. That's probably why the first 25% and "next part" have the rules of thumb that are given in the OP.