Would you mind sharing who wrote the article/what article you read?

My understanding of mounted combat in Japan filtered in from the continent/Korean peninsula. As far as mounted archery goes, I'm not actually sure because the books/articles I know of I don't have on hand and I can't remember. I don't think it was directly because of the Emishi though. Here's why:

The early Japanese state was fighting with the Emishi around the time they wrote the first sets of laws. These codified Tang Chinese style conscripted militaries, primarily in preparation for what they thought would be an attack from the Tang. These, along with a lot of Ritsuryo policies regarding control of the population, weren't sustainable though for a couple of reasons.

1 - At this time Japanese "families" weren't structured at all like the Chinese. They had no definition of a "household", no one person to hold accountable for the household, and no good idea how many people constituted a household, which was the basic unit of measurement.

2 - They had no good bureaucratic apparatus to count or enforce anything outside of places they could directly control, which were essentially the immediate surroundings of military or civic installations. There is also no documentary indication that the laws were more than just ink on paper. The policies regarding land, taxation, and conscription just didn't work for very long.

So, while the central Japanese state did have an infantry-style army for a little while, it didn't last very long because the system supporting it imploded. It's also worth noting that most of the record that I've seen shows that the conscripted army was focused on Kyushu (to get control of the island and defend against the Tang - who never invaded).

But the emperors repeatedly sent armies to northern Honshu to fight the Emishi. I'm drawing a blank on how those were constructed though. I don't honestly know if there's documentary evidence available. That whole region's history during this period is really fuzzy to my knowledge. Later, and by that I mean around the 10th century, we know for sure that northern Honshu was the primary horse-raising area for the Japanese, and during this time the Emishi still basically dominated the area. They'd been technically defeated in the 9th century, but local Emishi leaders still headed that area.

It may be possible that access to the horses in the north allowed for the proliferation of mounted archery, but it also required a lot more wealth first to own/feed/care for a horse and second to have time to train to shoot a bow while sitting on one. Which is why certain families specialized as warriors, patronized by aristocrats (families with land titles (and thus taking in the tax income and corvee labor that would otherwise have gone to the state) or the emperor. A conscript infantry army, like the one created by the Ritsuryo policies, would never be able to fight from horseback let alone shoot arrows from horseback for simple logistical reasons.

Long story short, it's possible that fighting the Emishi allowed for mounted archery's proliferation, but even still I'm not comfortable saying it was the only or even the main cause of the shift. I am curious about the article you read though! A couple others that I've read and am fuzzily remembering some details from are "The Introduction of Mounted Archery into Japan" in Warfare in Japan and Armed Martial Arts of Japan: Swordsmanship and Archery. Samurai, Warfare, and the State in Early Medieval Japan kinda talks about the origins of state warfare, and I know it cites the Hesselink article, but Hired Swords discusses directly the privatization of warfare in the Heian period, which I believe is when you see the rise of mounted archery.