For a lab report involving measuring absorption with a spectrometer, I need to know the total volume of a yeast cell culture that is put into a cuvette so I can calculate μmol of [substrate] transported/min per mL of cells.

Starting with 10 mL of the culture, 3 mL of deionized water is used to wash the cells after centrifugation and resuspend the pellet in. Then deionized water is used to  fill the tube to the 10 mL mark. 1 mL from the tube is put into 8 different microfuge tubes, and after centrifuging again, 1 mL of pH 3 tris buffer is added. The tube is centrifuged again and then the contents are resuspended with 1.2 mL of pH buffer.

There are more dilutions, but these changes represent the different kinds of changes in volume that occur in the experiment (adding substances to the vessel and transferring a portion of the mixture to another vessel). So what is the final dilution of the original 10 mL of cells in this case?

After 1 mL is transferred to the 8 tubes, I only need to know the dilution for one of the tubes, since they should all be the same

after discussing this question with you on skype we analyzed that upto adding of buffers we have  1ml of the culture in 1.2 ml of buffer and after that you have added 0.3mL + 0.6mL +0.3mL which makeds the total soln as 2.4mL
1mL of the culture is now in 2.4mL
you have taken only half of it for the final reading
so you are reporting absorption of 0.5mL of the culture in 1.2ml