Mobile notifications

Is there no iPhone iOS push notifications? Testing out project management software for our company and I know that would be a deal breaker if it is missing. When I installed the app it asked for permissions to send notifications but I don't receive any when I create a task or do any activity. Is it because I am the user creating them? When I added an event I did receive an email but that was all, and through Google Calendar I believe. Do I have the settings wrong or is this not a feature?