The movement of the player depends on when you set your time keyframes.
Whenever you put down a time keyframe, it stores the current time in the replay (upper timeline). So if you put both time keyframes down at the same time in the upper timeline, then there won't be any difference in time which you can see during path playback.
E.g. if you want your player to move 5 seconds of replay time (upper timeline), you have to place the first time keyframe, then play the replay for 5 seconds and then put down your second time keyframe.
The time at which you put your keyframe on the button timeline only effects the time in the video at which the player starts moving, not the time (upper timeline) in the replay where the player starts moving. So if you put those keyframes 5 seconds apart on the bottom timeline as well, then those first 5 seconds will take 5 seconds of time in the video (the player will move in realtime). If however, you were to put them 10 seconds apart on the button timeline, those 5 seconds of player movement will be stretched out over 10 seconds of video (so everything will be in slow motion).
I hope that was somewhat understandable. It's always difficult to explain some concept that one already knows themselves very well to someone that potentially has no idea what you're talking about.
