Sorry for the confusion here! When a repeating action, any start and due dates on the action are pushed forward by the repeat interval. (Actions without a start date are assumed to have already started.)
When I set up a perspective like you described and some test actions with that repeat type, the action was moved from the "Due today" bucket and into the "Due tomorrow" one. Which may just mean my test case failed to tickle whatever caused what you saw; if you see something like that happen again, please
email the support ninjas - maybe we can figure out what's going on. Sorry for the trouble!
Regarding the start date - yep, by default, we start the item as early as possible on that day. There is a feature request open on adding a configurable default start time like we have for due times; if that would be useful, let us know and we can attach you to that request.
Regarding documentation, the "Setting up repeating actions and projects" page in the Help material covers this stuff (and was revisited recently in order to add info on the new repeat type), but if additional info would be helpful there, let us know and we can file requests on that, as well. Thanks!