I didn't even realise BitBucket wasn't originally an Atlassian product. What do you think makes it seem so seamless, or what makes Atlassian so good at integrating new products?
TBH I would say they are "ok" at integrating products. Until last year I worked at a company that used Atlassian products, and while they worked well together there were definitely a lot of points of integration that were missing which we felt should have been there. It's been getting better over time, but it's definitely not seamless.
BitBucket/JIRA/Confluence integration could be much tighter. BitBucket definitely feels like an island IME.
That said, it's most of what you want from Github at much more reasonable rates. So I'm very happy with it outside of the positive network effects of forking on Github (I rarely see a lib I want to fork on BitBucket).