Greetings to you,

Since the result for JEE Advanced 2019 is yet to be announced, the dates for JOSAA counselling hasn't been notified officially. The JEE Advanced is set to declared on 14th June, 2019 10:00 IST. As soon as the results are declared, the dates for JOSAA counselling will be put up as the notification on its official website within few days. 

Chandu, 

There's no official date announcement of JOSAA 2019.But it is expected to start after Jee Advanced result and most probably it will start from 24th June. 

Official website of Josaa 2019 is not released . Josaa 2018 website will be upgraded to Josaa 2019 after official announcement. 

So after 15-18 June you can check exact information on Josaa 2019 website. The link is same as you have given Josaa.nic.in.

Hope it helps