Without looking at the logs form the job i can only speculate as to whay this may have happened but it may be due to the following:
Convert to Full Backup on Indexing Failures option which may be enabled for this iDA. What this option does\means is that if an indexing failure happens (may have been caused by the killed job or just some other indexing issue which may not be easily reproduced) rather than the job sitting there in pending and not running it would convert the job to a full which would then write a new index and not depend on the contents of the older jobs index.
You can check if this option is enabled here:
From the CommCell Browser, right-click the agent icon of the client computer whose agent configuration you want to change, and then click Properties.
From the Index tab of the agent Properties dialog box, select Convert to full backup on indexing failures.
It is not a bad thing to have on but note that it will cause you to run a full if there is an index problem, its up to you to decide if you would rather have a full backup or have the job sit in pending and or eventually fail out completely.
That is the only user intiated option that would cause that to happen, and without looking at the logs for that particualr job i cannot say for sure what happened but depending on what the differential was doing and what it had or had not written to the index when it was killed may have caused some sort of corruption causing the new differential to not be able to determine what it needed to do from some sort of index issue and then convert to a full.
If this option is not on and you want to dig deeper into why this happened, up to you if its worth it or not since it seemed to be a one time thing based on your tests but could happen again, you will need to open a TR with support so we can investigate this fully with the logs\web-ex etc.