Why does signaling overhead for time synchronization scale up with the number of transmitter nodes in a multiple access system?
Let's look at it a bit more in context:


  Moreover, E-SSA (as SSA) has another major advantage over SA/DSA/CRDSA
  i.e. its truly asynchronous RA nature eliminates the need to maintain
  accurate slot synchronization among all transmitters unlike the case
  in SA/DSA/CRDSA.  
  
  The need for transmitter synchronization is a major
  drawback for large networks as the signaling overhead scales up with
  the number of transmitters independently from their traffic activity
  factor. 
  
  The capacity of asynchronous collision channel without
  feedback was investigated by Massey in his seminal paper together with
  protocols sequences for achieving the capacity boundaries [17].


If I understand well, this is not about frequency locking, but about time slot synchronization: the synchronization occurs on a time scale that is orders of magnitude higher than the oscillator period.

In time division multiplexing, there is a guard period at the end of each time slot where nobody should transmit, both to prevent interference and to allow synchronization. 
Because this guard interval is present at each time slot, the sun of guard interval times can be considered to be an overhead that varies with the number of time slots (i.e. for the max. number of users the system is designed for).