If the url shortener using same script like others i have an idea with that.
On the settings they can choose if the views will be global or per campaign.
Global - all shortened links are unite as 1 means if i click on shortened link my ip will be counted as view globally for 24 hours even if i click on different account it will be marked ad counted since the views are global.
For example
Campaign1 - all clicks will be marked as unique
Campaign2 - will not count since ip is registered globally
Per campagin - if they choosed per campaign means for every campaign all are unique views
For example
Campaign1 - 1 unique ip
Campaign2 - the same ip but also counted as unique on this campaign.
I Don t Think That The Shortlinks Site That O Used Support The Compaign View That You Have Mentioned
Because They Really Count The Number Of All Visitors But They Only Pay For A Small Number In The First Image Below You Will See Hundreds Of Views But In The Second One There Is Only 7 Views Count As Paid
Number Of Visitors
https://ibb.co/d2yNHpCounted Visitors
https://ibb.co/njzF3U