But it says you don't have reactions until the end of the turn, not the end of the round; so after your turn - immediately before the next turn, not immediately before your next turn - you can take reactions.
Turn and round are not interchangeable. Once your first turn ends, you can take reactions. In the first round, if you were high in the initiative order.
To be fair, your reading is a nice stealth-fix to the problem most people have with the assassinate feature, so I might go that route anyways, but I think it goes against the rules as written..