Right, so actually, both sources are correct. It is just that they are starting from different positions. On the scienceworld page, it starts with compression from T1 to T2, whereas in most resources, the first step is when the system is placed on a heating reservoir. Since the Carnot Cycle is, after all, a cycle, there is no real definitive start and end, and likewise, there is no first step and second step.
I might add, that it is helpful to memorize the type of process that goes with each step, but ultimately, understanding the process as a whole will put you in much better shape in the long run.
I find that
this video really does a good job of explaining the Carnot Cycle as well.
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