Historically informed performance feeds on research on the place, time, established practices, theoretical treatises, instrument construction limitations, interpretative styles, etc. where the music took place. The approach to interpretation is revised upon new discovery. Faster tempi (than romantically-inclined interpretations) are sometimes incidental outcomes, and not exclusive to Harnoncourt.
One ingredient for the observation, is at the time Harnoncourt was making strides in the 1950s, conductors were reading tempo markings of old music as if the metronome had already been invented (it is an early 1800s invention). Many famous pieces marked adagio, andante, largo, lento, (denoting a slow tempo) were performed comparatively faster than the romantic readings, as such markings were used quite liberally.
Another ingredient is that Harnoncourt had a unique reading of orchestral classical pieces that emphasized tempo and dynamic contrast (e.g. Mozart piano concerti, Beethoven symphonies), which may lead to perceive sections were played faster than usual.
And I don't think those traits were set on stone in his idearium. If he were alive today, my impression is he would revise his decades-old reading of Monteverdi's 1610 Vespers, perhaps with slower tempo, applying transpositions in the Magnificat, and refraining from doubling strings and brass in the Dixit Dominus.
That is to say, it's not really about tempo, or any specific performance feature, though that's all that may come to our ears, or that we may be able to understand without extensive music knowledge.