Then maybe the emulator developers implemented their own version of BIOS instructions to ship with the emulator.
Dolphin Emulator has the option to use LLE for the audio processor, but it until some months ago it needed a bios dump from the DSP for it to work. Then recently they made an implementation of the needed files under GNU public license. It's nowhere near as accurate as the original files but works, for some games. Actually in this specific case I think they only implemented one processor ucode, the one used in Mario and Zelda games, so for using LLE with other games you'd still need a dump. This is very difficult and most times not very reliable, but can be done.
You sure jpcsp emulator is LLE? I can't find direct mentions to that on google :/ If so, probably using the real BIOS would give better emulation.. I'm just guessing, tough.