Well, Fulbright ETAs (in Madrid, but I'm pretty sure in Valencia and Cantabria, too) always start work on Sept. 15th. There's always an orientation about a week and a half before. We had to be here on Sept. 5th at the latest, I think it was. We stayed in a residence hall for orientation for 3-4 days if I remember correctly.
As for the placement notifications, I can only tell you from my experience. Last year we received an e-mail (those who were in Madrid) stating that we were placed in secondary schools in Madrid. When Fulbright sent us the contract paperwork later on, it had our specific school placement. Because Fulbright has to work with the Comunidad de Madrid for placements (This is the case for Madrid. Cantabria and Valencia work on different systems.), they probably can't confirm placements until the Comunidad has got an idea of who is returning and they have gotten their placements squared away. I can't remember when we got our contract paperwork in the mail. It wasn't too long after the notification, so you should find out about placements relatively soon!
I hope this wasn't too confusing and that it helped some! It's all a bit complicated to be honest!
But as for your flight, I can't give you a definitive answer. However, based on last year's timetable, I would wager they'll want you here around the 4th, as orientation started for us on a Sunday. However, that's all up in the air, so you'll just to wait until they notify you!
If you have any other questions about the process or advice (things I wish I would have had more of last year), just shoot me an e-mail: j_hall06@yahoo.com
Good luck =)