I hope this information is usefull to you. Its taken from the official Yugi-oh page, in the advanced roules section, I think you are talking about prority, as you said the players are the ones go has priority, an the turn player has it first. But cause the chain resolution the other (non-turn) player is the one who usually benefits for it. If you change phase or step, it resolves the same way.
Here's the cuote with some examples.
Simultaneous Effects
Sometimes, you will have simultaneous effects attempting to activate at the same time, such as when
Mystic Tomato attacks
Mystic Tomato, or 2
Sangans are sent to the Graveyard at the same time because of
Dark Hole.
Whenever you have simultaneous effects, resolve them in a chain, even if they are Spell Speed 1 effects. This is a special case when Spell Speed 1 effects can be chained to each other, because they are all trying to activate at the same time and the players are not choosing to activate them.
If only one player has simultaneous effects being activated, then that player can choose the order in which they resolve.
Example #1:
Player A activates
Swords of Revealing Light. Player B controls a face-down
Cyber Jar and a face-down
Morphing Jar #2. Both effects activate simultaneously, and Player B chooses the order in which they go on a chain. Player B can choose to have
Cyber Jar be Step 1 (and resolve last) and
Morphing Jar #2 to be Step 2 (and resolve first), or vice versa.
If both players have simultaneous effects being activated, then the "turn player" (the player taking his/her turn) automatically has his/her effect become Step 1 of the chain. The turn player has no choice but to be Step 1 of the chain, although if he/she has multiple effects being activated, he/she does choose which of those effects is Step 1.
Example #1:
Mystic Tomato vs.
Mystic Tomato
Player A, the turn player, attacks Player B's
Mystic Tomato with his own
Mystic Tomato. Both monsters are destroyed and then sent to the Graveyard. Their simultaneous effects form a chain.
Step 1: Player A's
Mystic Tomato effect, because he is the turn player.
Step 2: Player B's
Mystic Tomato effect.
(resolve in reverse order)
Step 2 resolves first, and Player B Special Summons an
Appropriate monster.
Step 1 resolves second, and Player A Special Summons an
Appropriate monster.
Example #2:
Mystic Tomato vs.
Shining Angel &
Jowgen the Spiritualist
Player A, the turn player, attacks Player B's
Shining Angel with his
Mystic Tomato. Both monsters are destroyed and then sent to the Graveyard. Their simultaneous effects form a chain.
Step 1: Player A's
Mystic Tomato effect, because he is the turn player.
Step 2: Player B's
Shining Angel effect.
(resolve in reverse order)
Step 2 resolves first, and Player B Special Summons
Jowgen the Spiritualist from his Deck.
Jowgen the Spiritualist's effect prevents any more Special Summons from occurring as long as he remains face-up on the field. Step 1 would resolve next, but because of
Jowgen the Spiritualist, the effect
Disappears and Player A does not Special Summon a monster.
Example #3:
Witch of the Black Forest vs.
Witch of the Black Forest
Player A, the turn player, attacks Player B's
Witch of the Black Forest (in Attack Position) with his own
Witch of the Black Forest. Both players have 4 pieces of Exodia in their hand and the 5th piece in their Deck. Both Witches are sent to the Graveyard. Their simultaneous effects form a chain.
Step 1: Player A's
Witch of the Black Forest effect, because he is the turn player.
Step 2: Player B's
Witch of the Black Forest effect.
(resolve in reverse order)
Step 2 resolves first, and Player B retrieves the 5th piece of Exodia from his Deck.
The Duel ends. Player B is the winner. Player A, the turn player, never gets to retrieve his 5th Exodia piece.
Example #4:
Black Pendant vs.
Sangan/Exodia
Player A, the turn player, has
Sangan on the field and 4 Exodia pieces in his hand, but only has 400 Life Points. Player B has a monster equipped with
Black Pendant. Player A activates
Dark Hole. All monsters are sent to the Graveyard. There are two simultaneous effects:
Sangan's effect and
Black Pendant's effect. They form a chain.
Step 1: Player A's
Sangan effect, because he is the turn player.
Step 2: Player B's
Black Pendant effect.
(resolve in reverse order)
Step 2 resolves first and does 500 damage to Player A. Player A has no Life Points remaining. The Duel ends and Player B is the winner.
(Had Player B activated
Dark Hole during his turn, then the chain would have been reversed,
Black Pendant's effect would be Step 1, and Player A would win with Exodia.)
