No, the dedup table will not automatically move to the SSD. And no, their is no command to move it manually. New entries will use the new special vDev for the dedup table, but existing entries will stay where they are.
Next, the special vDev for the dedup table, (your SSD), should have the same level of protection as the main vDevs. If your main vDev is RAID-Z2, (meaning 2 disks can be lost without data loss), then you would need a 3 way mirrored special vDev for your dedup table, (aka 3 SSDs in a mirror). Otherwise you are setting up your pool to fail.
De-dup is not a suggested option for the casual TrueNAS user. It tends to perform poorly unless properly designed and managed. The fact that you are asking questions indicates you have less experience and may not have a well designed server for use with dedup.
However, it's your decision.