I never use Neji in move 1, too hard to predict interrupts...
Put Neji in the back, Tobi in move 1.
Use acupuncture in round 1, immobile only if you need it, and only after the char has proc-ed the standard action so the immobie carries over into round 2.
Acupuncture last 2 rounds , so the next round you can refre* if you want. or you can save main mistery and immobile later on...
If you put Tobi in move 2, you have to control both move 1 and 2 of opponent ( assuming he has more refines than you on all ninja)
Not everyone activates mistery as soon as round starts. so don't be too confident in interrupts.

You don't want the puppet in front row, they will just kill it instantly.

Kankuro Fire Clone
Sasuke Neji X
X Puppet X

I recomend like this, more chances the puppet will survive, but neji needs to be lucky.