This is a strange interaction that I saw come up recently, it seems like it should not work, but I cannot figure out why. If anyone knows where this line of play is wrong please let me know.
Here is the scenario: Player A casts "Tibalt, the Fiend-Blooded". It resolves, at which point Player A has priority and should be able to activate Tibalt's +1 ability. However, Player B can activate mana abilities before that even though they do not have priority, so Player B taps "City of Brass" to add one red to their mana pool, at which point City of Brass's triggered ability goes on the stack. Now, Player A has priority, but cannot activate Planeswalker's abilities or cast sorcery speed spells because City of Brass's trigger is on the stack. Player A passes priority and Player B casts "Shock" targeting "Tibalt, the Fiend-Blooded", killing it before Player A has an opportunity to activate any abilities.
Using card tags is mandatory in the Magic Rulings forum. Please check your private messages to learn how to use them. I've added them for this post.
[...]However, Player B can activate mana abilities before that even though they do not have priority, [...]
No, he cannot. Unless an effect or cost asks for a mana payment, activated mana abilities can also only be activated while having priority.
605.3 Activating an activated mana ability follows the rules for activating any other activated ability (see rule 602.2), with the following exceptions:
605.3a A player may activate an activated mana ability whenever they have priority, whenever they are casting a spell or activating an ability that requires a mana payment, or whenever a rule or effect asks for a mana payment, even if it’s in the middle of casting or resolving a spell or activating or resolving an ability.