Make sure you use column headings, and avoid blanks.
Because rows are associated with shapes, there are other ways to make sure your data is easier to work with in Visio. The first way is to make sure your data is organized as a table, with column headings at the top and rows below.
If you use a database, this is most likely done already. But if you are using Microsoft Office Excel, it's up to you to ensure that your data is structured this way.
In the picture, example A shows data organized into columns and rows with column headings at the top. This will work great. Example B might work okay, but it will be harder for you and Visio since there is a missing column heading and a blank row.