It may look like there's something magical in the way a cold hard seed sprouts into a plant, or all the little subsystems humming along in your body. But when you inspect further down there are explanations.
So I'd say if a scientist examined a magician and inspected with his instruments, he'd find some cause for the magical effects. The midi-chlorian thing for example.
But if he couldn't find anything, that just means he has the wrong instruments. A magician can detect magic, right? And presumably, detect other magicians. This is how the wizened old man finds a young apprentice working on the family turnip farm. So the magician has instruments that can analyze magic, and so find the root causes and methods of it.
At first blush you'd say the magician's stuff doesn't have to work the same way the scientist's stuff does. But there's no reason why they'd be different. After all, when the magician conjures up some ice, the ice still melts. Unless it's kept cold by continued application of magic, that is. Once you figure out where the ice came from, everything fits with known scientific laws.
So it's not like magic needs to be some separate mystical thing. It's just a separate set of instruments and has its own laws which are not mutually exclusive with those of the traditional scientist.
That said, if you go to college for 12 years to become a physicist, you should have to go to college for 12 years to become a magician of the same caliber. If your country already has a large population of physicists, it's easier to train new ones. Likewise for magicians. For that reason it may take a long time for a country specialized in one to grow into the other.
Societal pressures may inhibit a shift as well. Perhaps being a magician isn't seen as an honorable or otherwise valued profession. Or maybe there are religious strictures against it. Perhaps the laws governing magic are more strict because of an earlier, more conservative government.
It's also likely that if magic were more useful than non-magical technology, traditional scientists would interfere with it because they'd quickly become useless. When a magician can conjure an Unseen Servant to code for him 24 hours a day, or create detailed 3D holograms for an architectural firm, who is going to learn to program or learn CAD? You're better off just becoming a magician instead.
Because of this I'm more intrigued by why not everyone in a fantasy world is a magician. Given the opportunity you'd obviously choose that career. If it's an issue of people being born with it or not, I'm sure magicians could alter a baby to become magic-capable. And of course there are always people who lack natural aptitude and ambition, who are unable to achieve those things.
But if a magician can magically automate, say, a grocery store checkstand, why wouldn't he? The store pays three employees $16k a year each to man that workstation. If they have a magician automate the checkstand for a duration of one year they can afford to pay him $40k and still save $8k per year.
Once everything is automated, what do the dumb and lazy do? There are no jobs for them. Society would have to change. In that environment of absolute plenty, would the non-magicians form an underclass without the resources to interact with the money economy? Dystopian, unless you're a magician.
Or would anyone who wanted something just be provided with it? What if a few magicians decided to wander around buying property and installing vending machines that gave out free low-quality clothes, food, and drink?
Would there be laws concerning how much time you could spend in a holo-deck? Maybe no holo-deck on Sundays?