Same effectors differs when FBBIK initialized with different pose

[Shinao]

Scenario :
I use an idle animation on my character, apply FBBIK and save all the effectors rotation and position.
I use a sitting animation on my character, apply FBBIK and save all the effectors rotation and position.
Going from the animator to FBBIK there is almost no difference in, the character pose, for this setup that's great.

Problem :
When I apply FBBIK on my character with the idle animation and set the effectors position/rotation to the saved sitting one, the character pose is messed up a bit. Effectors are the same from the above scenario but the IK is a bit changed.

Most likely when initializing FBBIK some infos on the bones are stored and applied in the IK process but I can't see what by looking at the code.

Any advice for that problem, even a hacky solution would be great.