You can set specific values in the UM Settings in the XPhone Server web interface in order to achieve the desired behaviour.
Navigate to "UM > Voicemail > General > Advanced Settings" and add the following two values:
This value dictates new recorded voicemails to have the length of at least X seconds in order to count as a "recorded voicemail". Otherwise the voicemail won't be recorded and be set as "Did not leave a message".
This value causes voicemails, where the participant didn't leave a message (or a message that's too short, see the value above), to not be saved in the inbox. It also does not need to be deleted via the user's voicemail.
Disclaimer: The Toast and a Journal entry will be displayed even if one (or both) of the called values applies. The call still counts as a "Call", which causes the Toast and the Journal entry to appear.
After setting these values save and restart the UM Settings and Services.