thank you for the hints. I will take a look at this.
Though, it seems that activiti engine has major issues with inconsistency in handling dates or maybe date timezones or something like that. Otherwise i can not explain why process's actions start dates are handled fine, deployments date are not. And when process action completes end dates and start dates of actions are updated (handled) 50/50. In my understanding it should be all wrong, or it should be all fine.