Lol you are probably close!
We know the Senju and Uchiha formed an alliance. My guess is that Tobirama created it as part of a way to try and seal the deal of the alliance AKA: Bring back Izuna Uchiha.
However, upon seeing his brother under the orders of Tobirama, Madara couldn't stand it. Possibly maybee even the thought that Izuna had been under Tobirama's control (considering Madara was aware of how to break the contract).
Then, after founding the Military Police with good intentions, and seeing it start to bring the opposite effect, Tobirama may have tried to use it for the Clan once again. Sadly, he would die before he could carry it out (an assumption).
There is one plausible problem. Madara mentioned it was a technique designed to clear out a battlefield....with this thought it could tie into what Tobirama's Space/Time Ninjutsu was.
Since the Jutsu was designed to destroy a battlefield, Tobirama's Space/Time ninjutsu may have been to create an alternate space in which he could go to as the Edo's annihilated the battlefield. Only returning after the destruction. It wouldn't be as advanced as Obito's or Minato's as he'd be stuck in one pocket of space...unable to move. Possibly hand seals or an object was required unlike Obito or to an extent Minato (As they could move).
^^^ of course the above counter argument is only valid IF Madara was telling the truth.