Which is quite bizarre. It basically means that we don't really have a PM, just a facsimile of one from the time she resigns. Though I suppose that's been true for a while.
I think it is the common approach - so Cameron remained PM until May was identified as successor, likewise Blair and Brown (albeit in both those cases the process to find a successor was truncated). Same with Thatcher and Major, although the leadership process was already under way when she announced she would resign - in fact she remained PM until Major was confirmed as the new Tory leader.
The only alternative would be to promote the deputy PM (David Lidington) to be interim PM - however that wouldn't provide any greater authority to act in the role than May until a new leader is found.
So on the assumption the leadership contest goes the whole way - i.e. to a vote of the membership - we will effectively be in a holding pattern for several months in terms of progress on brexit.