Returns filed with unemployment benefits prior to the $10,200 exclusion should not be amended. The IRS has indicated it will refigure taxes on these returns and adjust the taxpayer's account accordingly. The IRS will then send any refund amount directly to the taxpayer.
The IRS has not yet communicated a timeline for making adjustments and sending refunds. Look for an official news release in the coming days: https://www.irs.gov/newsroom
For state returns in states that conform to the federal unemployment exclusion, you may still need to file amended state returns. Luckily, unemployment compensation is not a taxable income in California.