After some consideration I have realized that you can't. Within the constraints you've given us, you can't make this all-the-way plausible without a lot of extra work. Bear with me here because I know that's an unpleasant result.
You are phrasing this as a fixable biological problem. But you also have this race slowly becoming space-faring in an organic, natural way. Way before a race becomes truly space-faring (as opposed to our level of flinging tin cans around our star), they must have had tons of time with which to conquer genetic engineering -- we're talking thousands of years of practice messing with their own biology. We would therefore expect that they are biologically the best versions of themselves. Like supposing the fixable biological problem is "they're like humans with a way, way overactive testosterone production" -- well, they will presumably have found ways to engineer their DNA to reduce "testosterone production," whatever that means analogously to their biology. If they can do it with a pill then they can do it with a set of proteins. If the pill had side-effects they would have developed a mechanism that doesn't.
Your options would therefore seem to be:
1. They are newcomers to technology
They didn't become space-faring in a slow organic process. Some spaceship crash-landed on their home planet and they were able to reverse-engineer the warp drives but they are still technologically very backwards. They haven't figured out the genetic engineering yet.
This one is hard to arrange because often you need some technical know-how in order to reverse-engineer technology. If you can imagine dropping a train into the middle of 1000 BC, could its discoverers really figure out what it does? Would their metalworking be good enough? The same applies if we're analyzing some alien's technology trying to use it to learn space flight.
But you might be able to make it work with a sort of "pirate race" that just conquers others' spacecraft, and those pirates might indeed be Vulcan-ish -- heck maybe that's why they don't respect property laws; maybe those laws seem "illogical" to them.
2. The problem is not biologically fixable.
It might be that the problem is not biological. Maybe it's cultural, having to do with how they're raised. This species might have a strange social structure where all the children have to raise themselves together in a group without adult interaction. In the process they do not develop any innate discipline. Medication is only reserved for those children who cannot learn to cope with adult life after they start to interact with other adults and learn how to focus.
Or maybe it is biological, but it can't be fixed that way -- maybe their brains are wired with something other than neurons, call them Branch Fibers. The idea is that Branch Fibers can only work in a scattered way, so to apply those biological "cures" would not improve their focus--it would just make them think slower and slower until they stop. The process of totally re-engineering a brain for better scientific progress might be a longstanding open problem.
There are a lot of options here but they amount to the idea that a pill couldn't solve the problem in the first place. And you said it could so let's cut these options short.
3. It's not a problem.
In this case, the situation is not viewed as a problem in the first place. Like yes, children are scattered and unfocused and yes they need to learn how to focus, but that's a good thing--why would you want to change that?
Some of this is kind of like the previous one. For example if you think about the strange sorts of social structures that have evolved -- honeybees, wolf packs, anthills, human society -- it's not out of the question that maybe the biological "problem" has nothing to do with some hormone that's out of balance, but it's just how the species is biologically wired to raise its youth.
But some of it is more fundamental. So I come from a physics background so let me explain with a physics analogy. We don't normally talk about our scientists this way or advertise them this way, but one way to imagine, say, the achievements of Albert Einstein is that he got radically pissed off, that genius is 1% inspiration, 49% perspiration, and 50% aggravation. To eliminate that "negative" aspect in reality might doom us to never making revolutionary scientific progress. And I'm not saying that Albert ever showed those emotions to others, it's not a part of the historical record as far as I know, but you might imagine that that this is what was alive in him.
Let me clarify. Everyone who comes to a cliff they can't climb takes the downhill road away. You have to. Most such people then see "ooh there's a river down there, that leads to a lake," and so forth -- they find something else. But you have to get really pissed off at that cliff to keep returning to it week after week trying new strategies to get the heck up it. For Einstein at least in four of his major contributions (special relativity, general relativity, the equations to figure out Avogadro's number, and the EPR experiment) there is a common theme where the laws of physics said "there are two or more totally different physical mechanisms at play here, and you can't figure out which one is responsible."
That sort of thing apparently bugged Einstein so much that he kept returning and returning to those things, making mathematical models even though he stunk at math, just trying to break those systems. In the first case he was like "ARRGH what if reality just DOESN'T KNOW who's moving?!" and in the second case he was like "ARRGH what if NOTHING IS EVER REALLY FALLING?!" and in the third case he was like "AHA I FOUND IT SUCKERS, if we take Boltzmann's mathematics really seriously then the atoms that are too small to see could STILL induce a JITTER in the particles that we CAN see" and in the fourth case he was like "AHA I FOUND IT SUCKERS, my previous relativity theory says things need to be LOCAL and the LOCAL hidden variables theory predicts something DIFFERENT."
Of course he didn't say any of it like that, but I like to imagine that's what went on in his head. :-)
Similarly you might imagine that this ADHD scatter-brainedness has some sort of real purpose to these Vulcans such that they would never dream that you would want to get rid of it.
- Maybe it is absolutely necessary to compete in a set of games that they like to play recreationally.
- Maybe it is part of how they experience creativity.
- Maybe their language does not allow them to refer specifically to a thing in itself but is based on circumlocution, so they always have to ambiguously describe the thing they're talking about rather than just specifying it by name -- and maybe that requires a lot of free-association neurons to both speak and understand; fixing the biological problem would render you mute.
- Maybe they have a periodic biological urge to seek some sort of isolation in the wilderness away from the rest of their society where they suddenly find clarity on their life purpose, and these mark the various stages of life -- a kid who never had his/her first Calling would never have grown up. "You want to freeze a person in an adolescent brain stage while their body ages? Are you out of your mind?!"
But for whatever reason nobody thinks it's a problem that their brains are naturally ADHD-inclined, they just think that focus is a simple learnable skill that needs to be taught to every third-grader.