When using Numbers app, is there a setting to create a new column when user presses tab?
To add a row above the selected cells use the Option+Up Arrow command. 

To add a row below the selected cells use the Option+Down Arrow command.

To add a column to the right of the selected cells use the Option+Right Arrow command.

To add a column to the left of the selected cells use the Option+Left Arrow command.

On an iPad you can use the next buttons found on the screen