Why Cortana reminder's are just pop up with snooze and dismiss option and there is not alert tone or vibration ?
There should be an alert tone...
Some things to check:
In Cortana's settings, swipe down to and tap battery saver. Verify that Cortana can run in background except when battery saver is on.
In Quiet Hours, make sure it is off or that automatic rules aren't causing Cortana to notify you silently.
In Notification Center, you might try setting notification sounds to default -- each app will use it's own alert tones according to the type of app.
All settings are as expected but still no alert tone.