Trans-Atlantic segment's operating carrier rule should apply (which does not mean the first segment's allowance will be carried over to all segments). If your inbound journey is all in Economy, the outbound journey's higher allowance due to higher class would not apply. If this happened at your outbound, I agree with others that the agent probably made a mistake. Since your origin is LHR and the furthest ticketed point is PUJ, not in the US, so it seems that the US DoT exception does not apply.

By the way, to OP, AA and BA use different systems. They will always have different record locators.