Will the new mods go to work immediately?
Yes, it will start as soon as the the SE staff deems the election period is over.
Is there any structured training or is it all "on-the-job" training?
As far as I can tell, it's all on-the-job training.
Will SE's team still be minding the store, stepping in when needed?
Of course! The SE staff is involved with all SE sites to some extent, more so in betas like this one.
As for any "power shift", yes the moderators will gain access to some new tools and hold a higher status than they currently hold, but the community is still in control of the scope and such. Moderators are put in place to enforce standards set by SE and by the community they're a moderator on as well as to deal with problematic users, spam, etc.
For more information about moderation, check out Who are the diamond moderators, and what is their role? and Stack Exchange Moderator FAQ