I think that you missed the correct definition of "right". M-W gives two that could work here:

2: in the exact location, position, or moment : PRECISELY
// right at his fingertips
// quit right then and there

4: in a direct line, course, or manner : DIRECTLY, STRAIGHT
// go right home
// came right out and said it

And the appropriate definition of "on" is:

c—used as a function word to indicate position in close proximity with
// a village on the sea
// stay on your opponent

I think that you missed the correct definition of "right". M-W gives two that could work here:

2: in the exact location, position, or moment : PRECISELY
// right at his fingertips
// quit right then and there

4: in a direct line, course, or manner : DIRECTLY, STRAIGHT
// go right home
// came right out and said it

"Come on" is not a phrasal verb here. "On" is a normal preposition, with the following definition:

c—used as a function word to indicate position in close proximity with
// a village on the sea
// stay on your opponent