http://software.ligo.org/docs/lalsuite/lalsimulation/modules.html

Hi Jolien,

Internally for the PE samplers, your second option is correct. 

The PE codes use the parameters (sorry for being pedantic, I wanted to have all 15):

thetaJN, the zenith angle between J and N 
phiJL, azimuthal angle of L_N^{hat} on its cone about J
tilt1, zenith angle between S1 and L_N^{hat}
tilt2, zenith angle between S2 and L_N^{hat}
phi12, difference in azimuthal angle between S1, S2
a_spin1, magnitude of spin1
a_spin2, magnitude of spin2
m1, mass 1
m2, mass 2
phase, reference phase
distance, luminosity distance
t_c, time at coalescence
ra, right ascension
dec, declination
psi, polarization angle

(Some slightly different combination of parameters is used for sampling, and the post-processing pages then derive even more parameters). 

The function XLALSimInspiralTransformPrecessingNewInitialConditions is then used to convert those internal angles to the S1x,y,z and S2x,y,z than the ChooseTD/ChooseFD LALSimulation routines expect. 
Look at: https://versions.ligo.org/cgit/lalsuite/tree/lalinference/src/LALInferenceTemplate.c#n1118 where this transformation happens.

Then it's a matter of what the waveform approximants do with those cartesian spin values (most set the coordinate system with z along L and x in the (L_N , N) plane, while some with z along L_N and x pointing from the lowest mass object to the highest mass object).

Cheers,
Vivien.