"Automatically detect changes" option is for the reading of the logging settings. It doesn't affect what gets saved or where or when, it affects whether Clarity will read the configuration at boot time only, or if it will re-read it whenever it might need to use the information (i.e. upon each occurrence of a potential log write, to see if logging is currently on or off for that level/category).
In v13, the option "Check for configuration changes every (seconds)" is for other parameters in the CSA and properties.xml file, however this will not 'make sense' for some parameters to change themselves on the fly (if you change the port the app service is listening on for example, you would still need to issue a restart for it to re-bind to different ports).
Pressing Save in the NSA/CSA should ALWAYS and IMMEDIATELY write any changes to the properties.xml / logger.xml, and if the DB is an a valid/installed state, to the CMN_CONFIG table as well (this table is the location of those files in a virtualized state for non-Tomcat environments). The NSA/CSA doesn't keep hold of any configuration changes for committing at a later date or anything, a Save is a direct and contained action.
As was mentioned earlier in the thread, you do have to keep track of multiple properties.xml configurations in a clustered environment however, to be sure you're updating all the ones that need to be done.
Edit: In case I misread the question, the 'automatically detect changes' option itself is written to the properties.xml file when pressing Save, it is the dynamicConfigurationEnabled property here:
<logger alternateDirectory="" dynamicConfigurationEnabled="true" traceAlarmThresholdSeconds="0" multitenantErrorReportingEnabled="false"/>