No. The term Effectively Connected Income (ECI) refers to the type of tax treatment (graduated rates) rather than the source of the income.
As a Nonresident Alien (NRA), you are only required to report and pay tax on U.S.-source income. Since "ECI" simply tells the IRS to tax it like a resident's wages rather than at a flat 30% rate.
As mentioned before, you only pay tax on the portion sourced to your time in the US, not the full income you earned from the RSU's.
@Mohit
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