IOS today widget problem

The due or available task would not be shown in today widget on the day it should be, if you didn’t open the app first.
Is it a bug?

It depends what you have set in your Settings under Today and Watch. It might be a bug, but if the change hasn’t synced to your iOS device yet it is expected. OmniFocus would have to sync to get the changes for your Today widget to be updated, which is going to depend on your sync settings, your connection on the device, if you are on the same network and many other factors. To check your sync log if you are waiting on incoming changes, go to Settings>Last Synced and what it says there. If the sync didn’t happen, the update to Today widget can’t happen. If the sync did happen, check where the item lives and make sure it is included in the Today and Watch items under Settings.

Last tip: If you ever get to a state where it seems like your Today widget isn’t updating, restart your device as the first troubleshooting step. It isn’t very common, but there are some rare cases where Widgets (of any kind, not just the Today widget) need to restart. Restarting the device is the way to restart all of the Today widgets as well as clear out all of the old requests to update them.