I am not a PSX programmer but I can tell you this : It generate sounds effect in exactly the same way as the SNES games (in particular the SNES Final Fantasy games) does, and do not do them the "PSX" way. In other words, sound effects are synthesized on the live using a simple set of sounds and changing their pitch/volume in real time as needed, combined with hardware effects such as volume enveloppe, noise and pitch modulation.
I was told that the PSX doesn't have dedicated chip to generate sounds from data, so there must be some sort of streamed data samples on the discs, no?
No. This means that the PlayStation does not have the equivalent of a SPC700, a dedicated processor solely to handle sound, instead the sound is handled directly by the main processor. However it does have a dedicated DSP, which happens to be very similar to the SNES' exept it handles 24 channels instead of 8, and that there is added feature, and the BRR compression scheme was slightly modified - there is blocks of 28 samples coded in 16 bytes instead of blocks of 16 samples coded in 9 bytes, but the principle is exactly the same.
Also, I'll add that it seem many PlayStation games by 3rd party companies seems to use a "standardised" sound engine made by Sony (or maybe by Psy-Q ?), FF7 definitely does not uses it, it seems to use a somewhat direct port/evolution of the SNES Squaresoft sound engines coded by Minoru Akao. (This apply to other Squaresoft Playstation games too).
From what research I have done, Final Fantasy VII seems to use the first 24 instruments of INSTR.ALL for it's sound effects, those are used for music as well. combined with the other remaining instruments.