As Marin, if you choose Empowered Mirror as your hero power, and your partner chooses Mystery Cube as their trinket, then every turn your hero power would replace your own trinket slot instead of replacing your hero power trinket.
This means that the trinket you buy on your trinket slot becomes erased, and you’re left with only 1 active trinket as Marin, since your hero power is now Empowered Mirror that doesn’t change, and your trinket is being swapped every turn.