Am I allotted dwell time after after a deployment before I go to Korea?

AR 614-30 is the reg you need to look in. I did not find anything specific to back up what you are being told.

Dwell time affects what your report date can be when placed on an assignment. If you were in Korea at the time you were placed on assignment your report would be the month following your dwell time end date. It sounds like you were placed on assignment prior to deployment and your unit chose to take you anyway. What should have happened is that you should have been placed on the Rear D instead

From what I understand IDT starts accruing on any dependent restricted deployments however I'm not sure if you need to have dependents to earn the time. The good news is if you do in fact get IDT it will roll over to your new command. I'm thinking once you PCS you'll end up in the rear detachment and would be there until you IDT is used and your new units forward element ask for replacements if any are deployed.