Will my Reddit & Quora ad be shown only on higher education pages on these forums?

No, the ads are targeted to the student, not limited to which content they are looking at.

Over the last years, advertising has shifted from "We have these pages you can buy ads on  that match the persona of who you're looking to target" to "We have this available audience for the targeting you're looking for and you can reach this audience across (or even beyond) our platform." 

This is, of course, much more valuable as you have many more opportunities to reach students on the platforms they spend time on.