The only problem was the configuration on Tomcat side. Since Tomcat doesn't use plain java.util.logging the config is little different. So adding some lines to conf/logging.properties helped:
...
handlers = 1catalina.org.apache.juli.AsyncFileHandler, 2localhost.org.apache.juli.AsyncFileHandler, 3manager.org.apache.juli.AsyncFileHandler, 4host-manager.org.apache.juli.AsyncFileHandler, 5reportExport.org.apache.juli.AsyncFileHandler, java.util.logging.ConsoleHandler
.handlers = 1catalina.org.apache.juli.AsyncFileHandler, java.util.logging.ConsoleHandler
############################################################
# Handler specific properties.
# Describes specific configuration info for Handlers.
############################################################
1catalina.org.apache.juli.AsyncFileHandler.level = FINE
1catalina.org.apache.juli.AsyncFileHandler.directory = ${catalina.base}/logs
1catalina.org.apache.juli.AsyncFileHandler.prefix = catalina.
2localhost.org.apache.juli.AsyncFileHandler.level = FINE
2localhost.org.apache.juli.AsyncFileHandler.directory = ${catalina.base}/logs
2localhost.org.apache.juli.AsyncFileHandler.prefix = localhost.
3manager.org.apache.juli.AsyncFileHandler.level = FINE
3manager.org.apache.juli.AsyncFileHandler.directory = ${catalina.base}/logs
3manager.org.apache.juli.AsyncFileHandler.prefix = manager.
4host-manager.org.apache.juli.AsyncFileHandler.level = FINE
4host-manager.org.apache.juli.AsyncFileHandler.directory = ${catalina.base}/logs
4host-manager.org.apache.juli.AsyncFileHandler.prefix = host-manager.
5reportExport.org.apache.juli.AsyncFileHandler.level = FINE
5reportExport.org.apache.juli.AsyncFileHandler.directory = ${catalina.base}/logs
5reportExport.org.apache.juli.AsyncFileHandler.prefix = reportExport.
java.util.logging.ConsoleHandler.level = FINE
java.util.logging.ConsoleHandler.formatter = org.apache.juli.OneLineFormatter
############################################################
# Facility specific properties.
# Provides extra control for each logger.
############################################################
org.apache.catalina.core.ContainerBase.[Catalina].[localhost].level = INFO
org.apache.catalina.core.ContainerBase.[Catalina].[localhost].handlers = 2localhost.org.apache.juli.AsyncFileHandler
org.apache.catalina.core.ContainerBase.[Catalina].[localhost].[/manager].level = INFO
org.apache.catalina.core.ContainerBase.[Catalina].[localhost].[/manager].handlers = 3manager.org.apache.juli.AsyncFileHandler
org.apache.catalina.core.ContainerBase.[Catalina].[localhost].[/host-manager].level = INFO
org.apache.catalina.core.ContainerBase.[Catalina].[localhost].[/host-manager].handlers = 4host-manager.org.apache.juli.AsyncFileHandler
com.prodyna.reportExport.level = FINE
com.prodyna.reportExport.handlers = 5reportExport.org.apache.juli.AsyncFileHandler
# For example, set the org.apache.catalina.util.LifecycleBase logger to log
# each component that extends LifecycleBase changing state:
#org.apache.catalina.util.LifecycleBase.level = FINE
# To see debug messages in TldLocationsCache, uncomment the following line:
#org.apache.jasper.compiler.TldLocationsCache.level = FINE
So i added an aditional handler "5reportExport.org.apache.juli.AsyncFileHandler" to get my stuff into seperate file. Then i configured this handler like the others. The crucial part is at the end:
com.prodyna.reportExport.level = FINE
com.prodyna.reportExport.handlers = 5reportExport.org.apache.juli.AsyncFileHandler
This uses the configured handler for all classes in package com.prodyna.reportExport.