Question: Does the wall get pushed out the same way we pick, to the right?

Answer: Tiles are picked by players in counter-clockwise (to the right) order, the opposite of card games. The walls are pushed out by the players to the left, in clockwise position.

This playing sequence originated in Asia where all players take turns in a counter-clockwise order and seat-to-Wind assignments given to seat positions. Most Westerners reference the East player and think more in terms of player numbers rather than seat-to-Wind assignments. To Westerners, the seat-to-Wind assignments can be confusing and seem backwards. You can use this mnemonic to remember the ESWN order, “Eat Soup With Nuts.”

Source: Mah Jongg Made Easy 2020 page 11 para. 1