If your circuit has multiple valid solutions (as many do) then
accuracy and method choices, coupled with the vagaries of
numerical solution goal-seeking, can give you different and
yet valid solutions; error residues can be different and then
differently amplified, etc.
Multicore is all abotu solution speed, and speed-first often
means looser accuracy defaults and more error residue at
every solution-point. You might try enforcing total consistency
of solution method, steps and tolerances and see what results.
You might want to look closer at the "wrong" solution and
how you got there, because it may just be "unexpected"
and waiting to emerge in your design validation sample
in real life.