A very very few independent contractors might operate on the "accrual" accounting basis, which means you book revenue when earned rather than paid. This is complicated and usually requires an accountant to set up, you would know if you used this system.
Everyone else, whether self-employed or a W-2 employee, is considered a "cash basis" taxpayer and you report income when it is actually received and expenses when you actually pay them, regardless of when the work was performed.