Special and general relativity postulate that all of us are embedded in a geometric/mathematical structure called spacetime.
Length contraction is not caused by the fact that the atoms are "shortened". It is space itself - containing the atoms - that is being contracted. In the end of the day, atoms of a moving object will appear closer to each other than if the object is not moving. But that is because they are inside space which itself is contracted.
From the perspective of someone located on the earth, the clock of a travelling muon is running slower than clocks on earth. So you would come to the conclusion that it reaches the ground at say 4 microseconds.
From the perspective the muon they are not moving, hence they will say that your clock is running slower. Still, they would agree that they reach the ground after 4 microseconds because the ground is being contracted towards them due to length contraction.