If you have 2 issues (lets call them "A" and "B") and you've created a dependency relationship between them so that "A" blocks "B" then the auto-schedule function will take that dependency relationship into consideration.
However, there are 2 modes that you can configure in a plan for dependency scheduling. The first is "Sequential" which means that dependant issues must be assigned to different sprints and the second is "Concurrent" which means that dependant issues can be scheduled to the same sprint (if the sprint capacity can accommodate both of them). The Auto-Scheduler will set start and end dates that match the start and end of the assigned sprint so for concurrent scheduling it will appear that dates have been set the same for both A and B.
I would recommend checking your scheduling configuration for your plan to see what mode you are using. Please let me know if you need any further assistance!
