Come on! "Till" and "until" are interchangeable here. But the "correct solutions" section says only "until"
I believe Till is not right (but it is, as you see in Davu's comment), it's one of those accepted mistakes in spoken language.
As far as I know they are synonyms. There is some justification here: http://www.oxforddictionaries.com/definition/american_english/till (I chose the American English definition because Duolingo uses American English but the same applies in British English).
I didn't remember "till" ever meaning "until" (but yes, 'til is the abbreviated version), so I double-checked in my OED (hard cover version), and that's what it said.
I won't be using till or 'till to mean until, but 'til we come up with a better option, until works for me!
Is "espera" also correct, for "tu"? I understand "Espere" is for "voce" ? There is vire and vira in this lesson , so maybe also espera and espere are both correct?
The closest sentence to what you suggest would be "Espere até A manhã de amanhã." But in spite of being correct it would sound a bit unusual.