my oppenent played a card in their turn, then they played astral heron to a battlefield does the next card get a discount

No — the discount never triggers.

Astral Heron's "if I'm at a battlefield" is part of the trigger condition, and it's checked at the moment your opponent's first card is played (Rule 383.2.a.1). If Heron wasn't already at a battlefield then, no trigger ever fires — playing him afterward doesn't retroactively create the discount. The first card of the turn has already been played, so Heron will just sit there without doing anything. (FAQ #11906 covers this exact scenario.)