This is a place where the iPhone and Mac apps behave differently. Mac app will include any "remaining" projects or actions in the Due Soon list when they qualify. (There is a feature request open on making this a preference; email the
support ninjas to vote for it.)
iPhone app, however, only shows "available" projects or actions that are also due soon. (If folks want this to be a preference, or want the behavior to match the Mac app's, they should also email the
support ninjas.)
Bill, I wasn't able to reproduce your date-changing behavior - when I changed a start time so it was in the future, the action disappeared from the iPhone app's due soon list. If you've got repro steps, sending it to the support ninjas would be appreciated!