There is no different dates for other state counselling in Anna university.  It will happen on the same dates as others are going.  But there is an eligibility criteria as only the locals are allowed in TNEA counselling.

If you have studied from class 8 to class 12th in any other state other than Tamilnadu you will be considered eligible only if you are native to Tamilnadu and  born in Tamilnadu but studied in other state then you have to provide a certificate from Tamilnadu Government stating the same.

You are also eligible if you are a student belonging from other state belonging to BC category.

If you are a student who belong to other states but your father is a Central Government employee who is currently working in Tamilnadu then you are also eligible but you must provided digitally signed residence certificate.