http://www.usatoday.com/story/news/nation/2014/10/01/texas-ebola-patient/16525649/
Article on the Drudge states vomiting start at day 10. If he was admitted to the hospital on 9/28 with heavy duty vomiting wouldn’t that put the onset around the 18th? It would not be unreasonable to believe he was in contact with many more than 18 and probably more than 80 people in that 10 day timeframe.
It is not that exact for everyone.
Symptoms may appear anywhere from 2 to 21 days after exposure to Ebola, but the average is 8 to 10 days.
http://www.cdc.gov/vhf/ebola/symptoms/index.html
You’re looking for a predictable date for onset of symptoms and therefore contagion in order to estimate potential exposure. That’s understandable. But, onset of symptoms varies from one to the next.