The Billing Realization Report is based on the Invoice Date of the transactions. Time Manager typically displays transactions based on the work date of the transactions.  You may right click on Time Manager, click on Select Grid Fields, and place the invoice date and the Write Up/Write Down column on the grid in time manager.

Filter using the particular Client-Matter, if needed, and also filter by the Invoice Date and/or the work date of the transactions. You should be able to see the invoice date on any written down transactions. If the Invoice Date is not included in the report dates you used for the Billing Realization Report, then this particular transaction would not be included in your report.