Yes, that is exactly how it works. Give the InmateAid forwarding number to your inmate and have him add it to his approved call list at the facility. When he calls that number, it routes through to your phone while triggering the lower rate that InmateAid's number was chosen to produce.
InmateAid does not replace the prison phone system. Your inmate still calls through whatever carrier the facility uses, whether that is Securus, GTL, or another provider. What InmateAid does is identify a number that, when dialed through that carrier, generates a cheaper per-minute charge than your regular number would. The savings come from how the carrier rates different numbers, and the forwarding line gets you to the lower-cost tier.
In most cases the new number does produce savings. If for any reason it does not in your situation, InmateAid will reverse the charge. There is no risk in giving it a few calls to see the difference on your end.