Hi!
The ChainIK constraint implementation in Animation Rigging is based on the FABRIK constraint. It works well in runtime applications when applying to a pose that is already set in a configuration that is close to what you target (e.g. look at our sample scorpion tail that is slightly bent already so that it retains this shape in runtime).
If you want more control on the chain IK constraint, then you can implement your own constraint in Animation Rigging. We’ve shared a lot of resources to help with that in the past few years: