Generally a space is a small hole left by doing a chain on the previous row (or round). If my understanding of what you've written of the instructions is correct, you're going to do this :
Put your hook in the next stitch, yarn over and pull up a loop
-you now have 2 loops on your hook-
Put your hook (with 3 loops on it) into the adjacent stitch, yarn over, and pull up a loop
-you now have 4 loops on your hook-
Yarn over and pull through all 4 loops on your hook
Now, in my understanding, where it says at the very end, before the )*, to "go through the same stitch", you're working in 2 stitches per bubble (for lack of a better term)...the same stitch they're referring to is the second stitch of the bubble. So you're going to start your next cluster or pattern stitch in the second stitch that they had you put your hook through.
I worked up a tiny little swatch and this is how I interpreted the pattern.