It depends. We had scores automatically sent after the August 26 SAT, which were sent on September 12. One school is still sending emails that our file is incomplete. They usually send scores on Wednesday, if you don’t rush them, but there can be an additional two weeks on the school side for them to process. You never know. One school sent an acceptance two days after the scores were sent an another is still saying they haven’t been received almost two weeks later.
You’re probably fine and you have enough time, it’s just a current frustration for me.