To understand the movie's ending, let's first look at the time travel rules presented. In effect, the radio very loosely follows the idea of a multiverse, implying that there are infinite parallel versions of our existence happening all at once. The version we're in now is based on the choices we've made, and because time is linear, they can't be changed — unless, of course, you have a time radio.
The movie also goes a step further to create a sort of "temporal bubble" for John, when using the radio, to avoid some obvious paradoxes. For example, if John warns his father about his death and then he survives, he wouldn't know to warn him in the first place, since he never died. To avoid this, John is allowed to keep his memories of every timeline shift he experiences. This bubble also keeps the realities that both John and Frank inhabit connected. For example, if John warns his father and saves his life, it could create a brand new timeline where Frank lives a long and happy existence, but leaves our John in his current reality where his father still dies tragically. As it stands, both John and Frank are linked to the same parallel world every time a shift occurs.
