Unless your company uses accrual basis then you recognize income and expenses when money changes hands. And unless your company has a non-calendar fiscal year you recognize income in the year it was earned/received depending on accounting method.
The vast majority of self-employed and small companies are on cash basis and use calendar year for their fiscal year. You'd know if that weren't the case for you, so if your 1099 is for 2019, you include that income on your 2019 tax return, and offset that income with business expenses you incurred in 2019.
The main benefit of the IRA contribution being allowed for prior year up to the tax deadline is that it gives you time to assess your tax situation before having to decide between Roth and traditional IRA.