If you are working in India for foreign companies, then you are allowed to accept compensation or remuneration in India. Those who are resident in India for tax purposes have to report their global income in India. Hence, this compensation must be included in your tax return filed in India.
Your employer may deduct some taxes at source or you may have to file a local tax return in that country. If that case, you will be allowed to take credit of taxes paid outside India while filing your Indian tax return. Make sure you include this income in your Indian tax return and make other disclosures and provide all the information required to become eligible to take credit of foreign taxes paid.
My daughter left India in September 2018 for a job abroad. Will she be taxed in India for the income she earns abroad?
Whether your income will be taxed in India depends on your residential status in India.
Residential status must be checked for each FY. This is how residential status is established in India for tax purposes:
You are resident in India in two of the 10 FYs immediately preceding the relevant FY, and you are in India in the seven years immediately preceding the relevant FY for 729 days or more.
If you meet any of the first set of conditions and both the additional conditions, you shall be considered a resident in India. If you meet any of the first conditions but do not meet the additional conditions, you shall be considered a resident but not ordinarily resident (RNOR) in India. If you do not meet any of the conditions, you shall be considered a non-resident in India.
However, condition b) does not apply to Indian citizens who have left India for employment abroad. Since your daughter has left India in September 2018, you must calculate the exact number of days spent in India by her in FY2018-19 and accordingly identify her residential status.
Those who are residents in India must pay tax in India on their global income. RNOR and non-residents are not required to pay tax in India on income which is earned outside India.