Yes, in most case MySQL follows system time zone. If your system or server has set to UTC time zone as default then every inserted date-time field will be automatically converted into to the UTC automatically.
You can either set/change timezone of system or MySQL. Or simply alter Insert (or EDIT, DELETE) query like below.
INSERT INTO tbl_name (date_time, first_name, last_name) VALUES (CONVERT_TZ(date_time_value,'+00:00','+05:30'), first_name, last_name)
It will save your Indian time as it is.