Our 2015 Prius Four came with an AudioVox remote-start device installed, which, IIRC, was activated by pressing the lock button on the OEM fob three times. I did try it once many months ago, and it worked. I tried it again a few times today, but all that happens is that the brake lights flash a few times, but the car remains OFF. I think that at one point I did reset all the customizable settings and have never noticed one related to remote starting, but did I perhaps miss something? (I can't find the brief instructions for the remote start feature at present.)
It's called a dodgy installation. Happens all the time. Good luck getting it repaired. The Toyota dealer won't touch it.