10% increases are maybe a bit conservative, but a quick Google will produce many examples of training plans that use that rule of thumb.
Does that mean it makes sense? For cycling? It's a lot conservative (Especially, for cycling).
The first link that Google returned (for me) for "ten percent training":
http://running.competitor.com/2013/10/training/the-10-percent-rule-fact-or-fiction_42570
It doesn't seem you actually looked at any of the links you found.
It's mentioned mostly regarding running and about half the links are critical of the idea. It seems mostly based on "folklore".
People are repeating it but they clearly don't know much about it.
And, for the OP currently riding 20 miles and wanting to do 100 miles in a month, it's useless advice. That it is unnecessary too makes it odd that it was even mentioned. It's strange that people are defending that bad advice.