The answer is in your quote.
...they will use 20 Raptors and use the navigation computer/organ from one of the captured Heavy Raiders to calculate the jumps back to Caprica. Using this, they can make it back to Caprica in a series of 10 jumps.
They did not use the FTL drive, they used the navigation computer to calculate the jumps.
Colonial FTL performance can be improved, demonstrated when a Raptor is successfully refitted by a team apparently led by Lieutenant Felix Gaeta with the navigational computer from a captured Heavy Raider (presumably the one used by Kara Thrace to return from Caprica in "Home, Part I") and, with the cooperation of a Number Eight, is used to navigate a squadron of Raptors back to Caprica on a rescue mission to retrieve a group of resistance fighters (Lay Down Your Burdens, Part I). A massive distance that would have taken Galactica 241 jumps one way (~482 jumps total), the Raptor squadron does in only 20 (10 to Caprica, 10 back).