There are two types of income that you can use in YNAB:
The income options in the Budget Category field are based on the date of the transaction. For example, if the transaction date is a May date, the choices under income in the Budget Category field will be Income for May (the current month) or Income for June (the next month). The amount entered will appear in the header of the month chosen on the Budget as Available to Budget. Learn more about recording income.
If you don't see the breakdown at the top of the month on the Budget then click on the Available to Budget number to expand it and view the income you've entered. That number will represent all income categorized for that month regardless of the source.
YNAB is more concerned about when money goes to work. Our goal is to help you out of the paycheck to paycheck cycle so you can Live on Last Month's Income. When you first start, you probably won't be able to do that, so all income needs to go to work immediately.
Eventually you'll save enough so this month's money can be deferred until next month. We call that having a Buffer. At that point you won't need your income for this month and can defer it to the next month.
You can use the Payee and Memo fields to record where the money came from or what it was paid to you for. Both of which can be searched with ease in the All Accounts view to locate any specific source and the Payee name will be added to your Income v. Expenses reports automatically.
Regardless of whether you categorized income as for this or next month the Income v. Expenses report will always show the income in the month the event actually took place.