Actually there is evidence that suggests that
chickenpox vaccination does increase the likelihood of getting shingles as adults. The article is odd because it sidesteps important questions like why on earth would vaccinated children be getting shingles as adults and why the incidence of shingles has been rising after the introduction of vaccination in the US.
You're reading that article wrong.
The article is poorly written, so you get a pass. It's so poorly written you almost deserve a gold star for being able to even make out any anything resembling an actionable conclusion even if wrong.
There's a reason the follow-up questions you asked are never addressed, because the questions rely upon drawing the wrong conclusion. For starters, the article is not saying that those youth who get the vaccine are more likely to develop shingles later in life. What it's suggesting is that a high rate of children getting the chickenpox vaccine means that, in the same span of time, adults are more likely to develop shingles because they are less likely to be exposed to children infected with the virus.
Which also means that the assumption here is that being re-exposed to the virus by infected children means you are less likely to develop shingles in any near-term period of time. What I get from the article is that adults who previously had chickenpox, when freshly re-exposed to the virus via infected kids, see their immune system kick into gear a bit and help ensure they don't develop shingles for perhaps two years. In other words, the assumption is that adults are fairly likely to be re-exposed to chickenpox every few years -- which in my interpretation means that this is partly why fewer younger adults (20-40) develop shingles, when they had had chickenpox as youth, because they are more likely to be re-exposed. Those who had chickenpox while young and are now 50+ have been more likely to develop shingles versus younger adults, and so I'm wondering if this is because of likelihood of re-exposure as opposed to some assumed immune system weakening that happens as you enter and endure the senior years. Which now that I think about it, that's an interesting theory that I hope someone runs with.
The conclusion here is that, by increasing the rate of inoculation to chickenpox in the youth, adults are less likely to be re-exposed naturally, and so that increases the incidence of shingles developing in younger adults compared to the norm.
This article also makes no mention of the adult shingles vaccine, which acts as a massive re-exposure for those who already had chickenpox. I assume that the adult vaccine represents a re-exposure event that produces a longer-lasting immunity than you would find in those naturally re-exposed.