Okay, I'm not good at patterns, and probably someone else will explain better...especially since I haven't done this one.
But if you look at the chart on the website, it says start with the last bit of the handle( as you said you did), then cast on 10 more stitches. At that point, take the stitches from the other end of that handle, and knit them next (so you'll have the 10 stitches from the handle, the 10 you cast on, and then the 10 from the other handle.
Then you continue casting on by adding another 26 stitches, then add the 10 stitches from one side of the other handle, then cast on another 10 stitches, then add the other side of the handle, then another 26 stitches.
It's like you're casting on 112 stitches to knit your bag, only you're sticking the handles in there at the appropriate places rather than sewing them on later. If it weren't for the handles, you'd just cast on 112 stitches. The instructions just tell you where to put the handles.
Does that help?