First up I should say that, as with a user-centered design project, we're open to iterating on this diagram. Feedback and requests for clarification help us scrutinise and improve, so thank you for challenging us!
Second, it's my experience that no project follows the same, identical process. This is something that threw me a little when I first began. "But why? It's a process, you should follow every step, so that you can rely on it and get the great result that you know you can rely on it delivering!" I would ask. Until I realised that real life is more complicated than that. The product being designed is different between projects; the project team is different—personalities, size, levels of expertise; time and/or budget may allow for certain steps in some cases, but not others; the assumptions you have about the target audience and what is important to them may be spot-on in some projects, and wildly wrong in others; and there may be political forces at play in the organisation that are beyond your control.
Basically, as UX designers we have to learn to adapt to the environment and make do with what we have. I mention all this because the question of whether one step occurs in a particular sequence or not becomes less relevant if your project is such that you're fighting to do any user testing in the first place. It's a rare luxury that one has the time, budget, and resources to run through a utopian process with sufficient iterations to produce the hallowed result. If you don't have a perfect scenario, you can't just walk away from the job and say "Sorry, I'm not going to help you." Some freelancers may be able to do that, but most of us will want to find a compromise and work with what we've got.
But I'm not avoiding your questions, honest! To the diagram and your specific questions about it.
* Beta Launch: It may make sense to add an arrow that bypasses the Beta Launch stage, and heads straight to Evaluation. It's certainly more likely that a project team will perform several iterations before having a product that is progressed enough to reach beta. Finding the right balance between keeping simplicity, accuracy, and flexibility is a challenge. The more I think about it, the more I'm tempted to remove the Beta Launch phase entirely, given it's implied by the fact that the diagram loops around for several iterations.
* Evaluation: What techniques are employed here? It depends on the product, of course, but one way to evaluate whether the first iteration of your prototype is headed in the right direction is to give it to users (or potential users) and observe them using it. Interview them about it. Make use of that feedback loop that you began when you first started doing your research. There may be other metrics that you could evaluate here too (sign up rate? conversion rate? task completion time?).
* User Tests: The answer to your question of "where does user testing sit?" is: that's what the arrows into the centre are supposed to indicate. Our little cartoon guy—the user—sits in the centre (user-centred, you see!) and he (well, ideally you'd have more than one) provides feedback at each of these phases. During research it may be via interviews, or journals, or surveys, or user testing of the existing site; in other phases he or she may participate in co-design sessions, or review storyboards, prototypes, competitor sites and give feedback on them. There will probably be some more user testing in those later phases. As you can see there are multiple ways to include users throughout the process. I could list several of these next to the arrows, but I decided not to as I didn't want to imply that any one technique was right for any particular phase. It depends on the project!
* Heuristic evaluation: Should this diagram include an heuristic evaluation? No, I don't believe so. This technique is only used when evaluating an existing product, when there is not enough budget to observe actual users, you know, using it. Plus it's only relevant for redesign projects, and irrelevant for a product that is being designed from scratch. They have their place, but in my mind they operate outside of the standard UX process, as they are an exception rather than the rule.
I hope that clears things up for you a bit. A while back I wrote [a blog post about process, actually, and included some other diagrams that may resonate with you if you're having difficulty understanding this one. At the end of the day, the order you do stuff in needn't be a rigid affair; so long as you're employing the techniques(http://uxmastery.com/what-does-a-user-centred-design-process-look-like/) that you need to include users as you progress through your design, and you take their feedback on board as you make decisions, then you're following a UX process, and you're giving your product its best chance at being loved by its users.
And that's the end goal, right?