The system shouldn't be in the tags. It should be mentioned in the body though.
The community has gone back and forth over system tags for a while, but the current consensus I'm aware of is that questions do not always need a system tag. As a rule of thumb, if the system is merely "background" information it doesn't go in the tags. That goes for any tag—if it's merely background context helpful for the answerers, but not what the question is about, then it doesn't go in the tags. At best, it gets mentioned in the question body.
In this case, the system is background information. The asker doesn't want or care about system-specific information, and is asking about the general concept of hidden rolls.
Our consensus on making questions narrower doesn't apply here
This isn't a matter of the original asker making the question artificially broad out of a misguided sense that it would help more people. The question they have simply is relevant to most RPGs, as it's about one specific detail of how people can handle rolls. The question is comprehensible and complete without system information—it's not "missing" their real problem behind an artificial broadening.
The concept of hidden information "leaking" into the metagame is a specific, narrow issue that we can have questions about, just like a question about how to play women as a man is a general concept applicable to many RPGs, but is itself a valid, narrow question without having to stick a system tag on it.
In fact, we have a community custom where, when people ask a generally-applicable question where it seems the system is merely secondary, we will advise them to remove any system tags so that the question gets wider viewing. This is exactly the sort of question were we would have done that if they had originally tagged it [dnd-4e].
So, this question is the inverse of the case in our narrow-question meta: if their (not-too-broad) question is naturally general, should the asker narrow it down to their specific system when possible? The answer is the same: no! The asker should ask the question they have.
This asker is already off the D&D 4e plantation
The asker has implemented fumbles in their game. People seem to really hate that fact, but the question isn't asking for people's opinions about that. People seem to really, really want to tell them they're doing it wrong—but they shouldn't, because the implementation of fumbles is presented in the question as a mere background fact, a given. And since they're already not playing 4e "right", the relevance of the [dnd-4e] tag is even weaker than normal.
They're not asking for us to pass judgement on that house rule, they're asking how to handle player knowledge when the player would know from the roll information their character wouldn't. A question that would be substantially unchanged without the fumbles, note. In fact, this is exactly what a high-voted answer did: passed judgement on the house-rule without even answering the actual question. That is a terrible failure of the SE system.
The asker didn't want it to be system-specific
The asker originally declined to put a system tag on it, on purpose. When asked, they said that the system isn't the important part of the question, the important part is the issue of character-player knowledge differences. They added the tag only afterward—but of course they did, because the comments were conveying the impression that it's a big damn deal and they'd done it wrong.
Based on the asker's own words identifying the core of the question, it might (at best) call for the system-agnostic tag. Though I don't think that's necessary either, since not every question on the site needs a system tag. Also, that would discourage mentioning D&D 4e in the answers, and we don't want that:
For helpful background context, the system deserves a mention in the body of the question. Answers can and should primarily address the general principle of how the GM should handle players gleaning "hidden" information based on seeing the roll—the core point of the question, the real problem they have—but adding 4e-specific implementation notes is a good bonus in an answer.