A Roth conversion done in 2020 is reportable on your 2020 tax return.
The US tax system is a pay-as-you-go system. See IRS Tax Topic 306 regarding the safe harbors for having sufficient taxes withheld or estimated taxes paid to avoid an underpayment penalty for not paying the taxes timely: https://www.irs.gov/taxtopics/tc306
The income is realized on the date of the distribution from the traditional IRA, so a distribution from the traditional IRA in July is 3rd-quarter income. The due date of an estimated tax payment for the 3rd quarter is September 15.