Yeah I think it is a little off. It is kind of like Quantum Leap but instead of leaping into other people he leaps into himself. Otherwise, you can't explain what happened to the other him a day ago. But if that's the case, how would he ever travel back to the save his mom? Leap into his kid's self? That could explain why his younger self ended up really far away from the crime scene. His older self leaps into his younger self, saved himself from the Reverse Flash by running way and leaped out leaving the kid having no memory of what really happened. But that won't work either because they found blood of his older self... oh well... I tried.
BTW, when Cisco revealed to Cold's Flash ID, I just thought, hey Flash could just go back a day and stops Cisco being picked up by Cold's sister. And I also think that the meta human jail is cruel and unusual punishment. Even murderers get to talk to other people and do things in jail. These people are in solitary confinement forever!