In Simulink, you can not start different subsystems at different time. When you start simulation at t=0, all block in the model will be executed based on their sorted order and will produce some output which will be input to succeeding blocks.
You can only control the output of the subsystem using Enabled Subsystem or Triggered Subsystem.
For example, place your reactor 2 in an Enabled subsystem and activate the enable input from t=X time (using Clock and Compare blocks). Until subsystem is disabled (before t=X) its outputs will have reset values defined in outports. When subsystem is enabled (from t=X) its internal logic will be executed and outputs will have calculated values.