Both of you start making sense right now!
You said that if a characters die once, they can't be considered "alive" anymore. Well, every Rider, including the original ones, died in Decade. So, according to your reasoning, even though they came back to life, they are still considered dead :loltongue:
Apollo Geist got saved, however since he is not a Rider he travelled to a distorted time portal, tripped on many dimensions and ended up on Let's Go Kamen Rider.
The Apollo Geist in Let's Go Kamen Rider is implied to be the original one, who was never destroyed since in that timeline the Kamen Riders failed at the very beginning (everyone from V3 to W was thrown out of time), the one that gets destroyed in Decade is simply an AR!Apollo Geist.