If 2 users attempt to make changes to a Defect at the same time the second user is warned that another user has modified the record and given the option to overwrite the changes.

This does not occur for Incidents.  The changes made by the first person are overwritten by the second without warning.

Is there a way to prevent this?

OnTime 2007 v7.0.2.7191

I was able to replicate this problem on our end as well. This has been classified as a defect in the OnTime 2007 application. The following problem will be addressed in the upcoming maintenance releases of OnTime.