So, can there be a message to the voters to carefully check if the possible duplicate can be applied successfully to the question without further modifications?
It happens sometimes and even in worse case than this one, when a duplicate is hinted at which is not applicable to the new question's setting or even solves a completely different problem.
What's the strategy you can adopt in this case?
First and foremost, when a vote for closing as duplicate is issued, a comment by the user who voted first is automatically added and you can reply to the comment, so that user can retract their vote.
However, as far as I know, that comment is removed when the question is actually closed, either by getting five votes or with the golden hammer. I'm not sure that comments addressed to one of the voters are notified to them, but that's certainly something you can try.
You can also edit the question explaining why the suggested duplicate isn't really good to solve the problem. The question will be bumped up in the front page and somebody may notice that the title has something like “not a duplicate” in it and investigate.
Maybe the duplicate is actually good and all it takes is some small change that can be added in comments (or in an answer to the duplicate) and in this case all is well. The title can be changed back or the question can be removed.
If after investigation it turns out that the question is not a duplicate, it will quite certainly be reopened. Wasn't it the case with yours?
There is an incentive to process content listed within the close vote queue, because there is a badge associated with it. It is, however, expected that reviewers will take the time to actually review the two posts and consider whether the one can be used (in some way) to solve the other.
However, the site allows for discussions related to inaccurate closures (like you did here on meta). Even if you didn't, an edit to a closed question (in this case stating that the suggested duplicate doesn't solve the problem and why) ends up in the reopen review queue automatically. So I don't think there needs to be a site-wide change/feature* to provide "a message to the voters to carefully check if the possible duplicate can be applied successfully to the question without further modifications."
Here is my suggested pathway for incorrect duplicate closure:
Edit your (now-closed) question stating why the suggested duplicate doesn't solve your problem. Effectively, you're showing the community you've tried what they suggested and it didn't work, and there's why.
The question automatiicaly goes into the reopen review queue where reviewers will read your reasoning and should vote to reopen.
If this doesn't resolve the closure, consider either posting on meta asking for some feedback - this is a valid reason to post on meta since the question deals with the site content; or
Visit the chat room where regulars are happy to support your efforts (like reopening or otherwise) and discuss things like ducks.
* Features are not child-site specific, but rather network-wide. So a request for that should, if valid, should be posted to Meta.SE.