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You should get a signal the moment you install the device. If you don't it means that no theft will occur in this timeline. Or you may not get a signal at all depending if time traveling generates timelines (the alarm system travels back in time and then sends the signal to you).
@DavidLjungMadison it depends on how time travel works in this question's reality... For example if the time machine 'teleports' you to the evaporation point you weren't there for the universe collapse so you skipped it.
As noted elsewhere banknotes usually have serial numbers... duplicating it on a global scale would likely push for banks to retire paper cash and replace it with electronic payment systems that would crash along the gold depreciation. So you might want to first devalue cash then crash the economy.
Being able to nag anyone at any moment is my wet dream as a telepathic troll. My Nigerian friends also convene that it would certainly facilitate their rightfully honest jobs in the financial market.