This may sound familiar. Try the following:
Take Smooth Sync off of your objects entirely.
Keep “Replicates Movement” off.
Does it still move around on the platform?
If so, there is something besides Smooth Sync setting the position that will need to be turned off. Only Smooth Sync should be setting the position or your Smooth Synced objects.
I think I heard of someone with a similar situation but I forget what they did to change it now. I’ll have another think about it if you reply that this is your issue.