The important test here would be to determine the individual's residential status for the tax year 2011-12, if the individual satisfies one of the basic conditions (i.e. 182 or more stay in the tax year 2011-12 or 60 or more days stay in current tax year and 365 or more stay during the 4 preceding tax years in India) and both the additional conditions (i.e. Resident in atleast 2 out of 10 preceding tax years in India and aggregate stay of more than 729 days in preceding 7 tax years) laid under Section 6 of the Income tax Act. The individual would qualify as a 'Resident and Ordinarily Resident' (ROR) and only in such a scenario would be taxable on his global income.
If your assignee, qualifies as 'ROR' for the tax year 2011-12, then he will be taxable on his global income including income from USA. However, he should be able to claim credit for the taxes paid in the USA on his India tax return as per the computation mechanism laid under the India- USA double tax avoidance treaty.
Note, if the assignee qualifies as 'Non-Resident' or "Resindent but not Ordinarily Resident' for the tax year 2011-12, then he need not declare his USA income, as his global income is not taxable in India. He is taxed only on income that is sources or accrued in India