Reg UC and council tax

Hi I’m just enquiring that when folk who are in esa support group are moved to UC by transactional migration Will they still get the full council tax support
As I am seeing in the forums on here that some folk are expected to pay nearly a 150 pounds a month as they don’t get the same full council tax support on UC as they did on esa support group
Is this true for every person being transferred from esa support group as transitional migration to UC
Also does any one else know if there is any more areas where less money is happening such as having to pay towards your rent when your on UC even though you got full housing benefit on esa support group