This Anomaly will make both players draw to 5 at the end of either's turn, killing you very quickly at fatigue.
If you have 3 cards and reach fatigue, you draw 2 at the end of your turn (3 damage), draw 2 at the end of your Opponent's turn (7 damage), then 1 at the start of your turn (5) damage.
I've observed this behavior as well. The wording clearly specifies that you should only draw at the end of your own turn, but both players draw at the end of any turn. It's very obvious on the first turn, since your opponent starts with less than 5 cards.
Anomaly - Refreshing: "At the end of each player's turn, that player draws until they have 5 cards."
https://www.reddit.com/r/hearthstone/comments/c2twtz/this_anomaly_will_make_both_players_draw_to_5_at/
I've observed this behavior as well. The wording clearly specifies that you should only draw at the end of your own turn, but both players draw at the end of any turn. It's very obvious on the first turn, since your opponent starts with less than 5 cards.