First, you probably shouldn't go by the kit instructions. They almost always rush your beer. Second, don't worry about moving to a secondary unless you'll be doing some long-term bulk aging, dry hopping, etc.
With that out of the way, the fermentation clock isn't all that important. Ideally, you'd want to pitch your yeast and have an active fermentation going shortly after, but it does take a day or two for some brews to really get going. That is fine. Either way, you should plan on leaving the beer in the primary bucket for at least a week or two. But the instructions say just 6 days? So what. Sure, you can still make beer after just 6 days in the fermenter, but give it a little more time and you will be rewarded.
Once you're getting ready to bottle just be sure to take a hydrometer sample a few days in a row and make sure you're close to your target gravity and see that the gravity hasn't changed after a few consecutive samples. This means your beer is done fermenting and safe to bottle.
You will have good beer.