Basically, upon a migration Stat invokes Oracle FNDLOAD utility to do the work.
So,run the FNDLOAD command outside of Stat, and probably will get the same result (same date).
Remember that the .lct file is written by Oracle.
To know what command you have to run,
1. Put the oracle agent in debug mode for the pertinent instance and restart the oa.
2. Perform the migration and in the log you will find the FNDLOAD command like below:
/<any path>/apps/apps_st/appl/fnd/12.0.0/bin/FNDLOAD APPS/password@alias 0 Y UPLOAD /<any_path>/apps/apps_st/appl/fnd/12.0.0/patch/115/import/<the name of lct file>.lct
3. Take this command and execute it outside of Stat.
4. Opening the object from Oracle Apps and compare the date. If those are the same then address the issue to Oracle Support.