You are correct, it is 2019 income to you, even though it is a 2018 expense to the payer.  If this is your only LLC or partnership income for the year, the IRS will definitely ask you about it.  If this is one of many, they may not notice.  This probably happens a lot, so I would expect that a simple letter explaining the issue and that you will report it in 2019, should be sufficient.