All card type have arrival fatigue, which means the turn they come under your control, they can't use abilities that require exhausting as part of the cost. If they are units or heroes, it means they also can't attack the turn they come under your control. If a card has haste though, it CAN attack and use exhaust abilities the turn it comes under your control.
Simplified, it means if the card is not under your control since the very beginning of your turn, it has arrival fatigue. — WildhornArrival fatigue is tied to the card itself, so if a Sirus Quince's Mirror Illusion has been under your control since the beginning of your turn and it copies something, even if the copied card has arrival fatigue, the Mirror Illusion doesn't. The opposite is also true, if you summon a Mirror Illusion and copy something doesn't have arrival fatigue with Sirus Quince's midband, the Mirror Illusion still has arrival fatigue. — Wildhorn