First, go to preferences and make sure that you have Synchronize time of related events checked so you can see what's going on in a nested comp. The CTI's don't match in your bottom screenshot so there's no way to tell what value the expression is giving to the second keyframe.
Second, set your time display to frames so that the time remapping values are digits. Do this by Ctrl/Cmnd clicking on the time display in the timeline.
Third, if the value in the slider control does not precisely match the value in the resulting time remapping, and they are nowhere close in your comp, then you'll need to add language to the expressions to convert the slider values to time. I don't have the time to give you the correct expression language but I suspect this may be the problem. You can't use the "slider" and drag it round to set your keyframes, you have to type in an integer or precise time value unless you write the expression to convert slider values to time.
I tried the two first items and the problem continues. To the thirt item, you are really right. But I don't know programing
Thanks for your help
If I get a chance later tonight I'll put up an expression. Don't have time to get to it right now.
If you want my archives to see better. I send to you.
Thanks for your help!