I am not a chartered accountant; trusting tax advice from random strangers on the Internet is not a winning strategy. The following is a summary of information from the Charity Tax Group's page on PAYE.
As an employee, the pay should have occurred during or around the time the work was performed. Perhaps the term "employee" is not correct for your situation -- perhaps you are a contract worker -- in which case, the following does not apply.
HMRC requires charities to collect Income Tax and NICs from empoyees' pay as it is earned. The charity pays these collections to HMRC under Real Time Information (RTI), except in very specific circumstances. A charity must operate PAYE on an employee if that employee's earnings reach the National Lower Earnings Limit (LEL). There are several specific limits, for example GBP 486 in a month.
If PAYE or PAYE:RTI is (or would have been in the normal course of reporting even if not reporting was legal) provided to HMRC on your earnings in the 2016-2017 tax year, that income is included in that tax year. However, you have no visibility into this process, so how do you know in what year the charity engaged in required reporting? At the end of each tax year, the charity must provide a Form P60 detailing income tax, NICs, and other deductions, even if these are zero. Thus, for each tax year, you have direct information from the charity. This information should match the pay stubs you receive from the charity for each payment of wages (and other forms of remuneration).