April 29, 2018 2:31 a.m.
No. Tiana, Ship's Caretaker is put dies, which causes Squee's Embrace to trigger. Then state-based actions are checked and Squee's Embrace is put into it's owner's graveyard, note that Tiana is no longer on the battlefield to trigger. Then the trigger is finally out on the stack, and once it resolves Tiana will be back in your hand while Squee's Embrace will be stuck in your graveyard. From Gatherer:
4/27/2018 If an Aura you control is put into a graveyard immediately after Tiana leaves the battlefield, most likely because Tiana left the battlefield but the Aura was put into the graveyard as a state-based action after it found itself not attached to anything, Tiana's last ability wont trigger.
April 29, 2018 5:56 a.m.
Neotrup's answer is the correct one. They don't actually go to the graveyard at the same time. See the Gatherer rulings note quoted above.