Once a player begins his hand by picking a tile from the wall, Joker exchange(s) can be done.
A player is entitled to doing a Joker exchange regardless of whether they are playing an exposed or concealed hand.
Once a player has begun their turn by picking a tile from the wall, they may do a Joker exchange or multiple Joker exchanges from any player’s rack including their own.
If you claim a discard to start your turn, you must be able to complete an exposure with the discarded tile.
Since Jokers can be named same when discarded, players must watch the table.
Abstract: The League recommends that a player not call a follow up tile that is identical to the previously discarded tile “same.” This ruling is not found in Mah Jongg Made Easy. Question from a player: When the same tile
Discarded tiles cannot be claimed to be used in a joker exchange.