Wow there’s a lot of different fan stitches I wasn’t aware of 
I found several that sort of look like that stitch the original photo says it’s a fan stitch so I went based on that and found all of these some might not look like it but may perhaps offer insight that could potentially help you, I think the stitch depends on the yarn, hook, and tension so while the videos/blogs may look different from the photo you provided, it could end up looking the same depending on those things
This one uses Spanish crochet terms but they’re pretty easy to understand, if you don’t do the picot at the top I think it’ll look like the photo, if you need help with the terms I can also give them to you as well
I hope these offered some insight, I think posting a photo of the swatches you make will help so I can perhaps see why the pattern you used isn’t coming out quite right we might be able to adjust the pattern you use to help get the look better!
Also something I try to do for newcomers, congrats on your first post 
if you ever need help never hesitate to ask in the community, if you need immediate answers feel free to use the help center, search in the community, or the wiki [link below] and community guidelines if needed Happy crafting! Hope to see your crafts soon as well