Thanks for the file!
I usually place the rnd(value; seed) into Formula fields, like rnd(123;456). However, if stable results are required, I can confirm that this is not working with the MoSpline.
I have to file a report about it.
Two option. Place a Create> Spline> Empty Spline into the Destination field, and at the exact moment you have a setup you like, switch the MoSpline off. Perhaps even clear the Destination field.
Of course, the Object Manager> Object> Current State To Object will do the same. But if the Spline (Segment) is used somewhere else, the CSTO option requires connecting the new results.
Setting it up via a Cloner and a Random Effector (set to Random Indexed) might allow for some workaround.
I'm curious what the reply to the report will be and if a fix is soon available.
All the best