It's done as stated. When the break between sectors is not a full rest period.
Sector on blocks +30 minutes rest starts, let's say 4 hours rest before resuming the next sector sign on (off blocks-1 hour). You can extend your normal days duty by 1/2 the time taken as rest.
Example original FTL 12 hours, 4 hours rest taken between sectors, you can now do a 14 hour day 12+ [1/2 of 4]= 14.
Simples.