The Webinar Takes a little time to load, My Last test i clock it at taking 2 minutes. After the initial browser window opens, it should try opening the Adobe Connect window in a separate window. after that opens, it will need to download the webinar before it starts playing.
As for needing to run Adobe Flash in un-safe mode, that is not a matter of the way the recording was made, but rather a limitation to Flash in Safari. In safe mode, adobe Flash cannot access the connect add in. see the following quote from adobe: