I agree on the power cards. But on the objective cards, Page 25 under "Objective cards in the action phase" it states that if you score a card in the action phase you discard it face up, gain the glory, then immediately draw another card. Quoting the relevant text: "If an objective card is scored during an action phase, that player can immediately draw another objective card."
Maybe this would only happen in the power phase and not the score immediate ones, but as written I feel like you would still draw for both.