I'm not using UltraEdit for Mac because I don't have a Mac whether physical nor virtual.
But I found How to Quit Mac Apps Without Closing Windows
. Do you have Close windows when quitting an app
unchecked at System Preferences - General
for your Mac?
UltraEdit for Windows has the two options Minimize on last file close
and Minimize on system tray (not taskbar)
at Advanced - Settings
/Configuration - Application Layout - Window State
. The second setting is definitely Windows specific while the first one could also exist for UltraEdit for Mac. Can you find in Preferences
of UltraEdit for Mac a similar setting or a setting related to application quit?