This is correct.From the Hasbro official Risk rules:
Eliminating an opponent. If during your turn you eliminate an opponent by defeating his or her last army on the game board, you win any RISK cards that player has collected.
* If winning them gives you 6 or more cards, you must immediately trade in enough sets to reduce your hand to 4 or fewer cards, but once your hand is reduced to 4,3, or 2 cards, you must stop trading.
* But if winning them gives you fewer than 6, you must wait until the beginning of your next turn to trade in a set.
* Note: When you draw a card from the deck at the end of your turn (for having won a battle), if this brings your total to 6, you must wait until your next turn to trade in.