Looks like the Betta did not produce enough waste to get the cycle started, then when you added the other 3 fish, it got going. So, you had a slow start and you have one tough Betta!
I just ran across an interesting vid on YouTube - do you know anybody else who has fish?
Unless someone gives me a thumbs down on this, I think we will try it next time we have to set up a tank. Cheaper than buying bio in a bottle and we have about 800 gals of tanks running - yes at our home - we are crazy and we don't even drink Whiskey :)