There's actually a component you can add to the object you're placing on the globe, it's called... Look at constraint (unbelievable). Without surprise, the blue arrow points towards the target so essentially the constrained object is upside down. You'll have to circumvent that, like for example with adding a child to this object that's pointing in the opposite direction from its parent. Or in Constraint Settings, unlock the object and put x:180 in Rotation Offset.
You may want to get the radius right first, by getting the globe's radius, using it as the distance [object to place]<->[planet center], place the object so its base touches the globe, then activate the Look at constraint (drag the component into a state and set its property), then activate and show the object.
The other hard part will require knowing how to extract the coordinates from the color map.