Was there a specific tactical reason, contextual, or overall strategy for it?
EDIT: There must have been a reason why this idea wasn't adopted in later mercenary armies.
I'm going to write a quick comment here because it's after midnight here. You are referring to the statistic that one in four (I have also seen "one in five") of the infantry of the Hungarian army in the time of King Mátyás I (Matthias Corvinus) was equipped with an arquebus.
It's important to remember that it was very rare at the time to have something like Mátyás's Black Army (a Fekete sereg), which was a standing mercenary army drawn from many countries rather than a feudal army provided by the vassals of the king. The excellent system of taxes (reformed under Mátyás) and contributions owed to the royal treasury made this expenditure possible. This allowed for a greater level of professionalism, training, and equipment. This in itself already explain much of the difference. Mátyás was also fond of the shield wall and its effectiveness in battle.
According to The Oxford Encyclopedia of Medieval Warfare and Military Technology, these are the words of Mátyás himself in a letter to the bishop of Eger (I realized after typing all this out that Wikipedia uses the same quote--sigh):
"Then there are handgunners.... These are very practical, set behind the shield-bearers at the start of the battle, before the armies engage, and in defense. Nearly all of the infantry and the handgunners are surrounded by armored soldiers and shield-bearers, as if they were standing behind a bastion. The large shields set together in a circle present the appearance of a fort and are similar to a wall in whose defense the infantry and all those among them fight almost as if from behind bastion walls or ramparts and at the given moment break out from it."
It is also worth noting that the "one in four" (or five) only applies to the standing mercenary army, which made up about 28,000 troops. The rest of the Hungarian army (which could number up to 90,000, according to some sources) was made up of allied forces, soldiers from conquered lands, and the usual feudal vassal units.