Whats the responsibility of Onsite lead?

I have worked in other Organisation's and i have seen managers and Onsite leads who will take care of project requirements and managing the team of juniors, and eorking with clients and Business Associates for requirement discussion and analysis then he/she will explain the Requirement to offshore team, if Business Associate is also onsite then he will be taking care of the meetings abd reviews, and offshore team purly work along with him and dont involve directly with client or business associate,

Thats my experience in other companies as offshore team member.

Comming back to TCS, out of above points nothing is done by onsite person, only offshore team has to update the status and track the defects. Even though there is 12 hours time difference in working conditions this on site person he still expect we have to respond to the mails then and there even at 1 am IST, which is not my working shift of offshore, we habe to connect the client calls in those odds hours and we have to change the on site Business person for requirements by waiting more than 3 hours in their time shifts, still the project mangers expect us to daily vist the office, even though we awake till 1 am for project work,

I wonder what else online person doing in his working hours!?