Yes, you are terminating T568A and then, testing T568B.
Just flip your green and orange pairs.
In the T568A pinout, the pairs 1&2 (white & green), and 3&6 (white & orange) are opposite of what the pinouts in T568B are. In T568B, the pairs are 1&2 (white & orange), and 3&6 (white & green). Both T568A and T568B have the same pinouts for pairs 4&5 (blue & white), and 7&8 (white & brown). In ALL pinouts the white wire that is paired with its colored partner is called the "tip", and the colored wire in every pair is known as the "ring".
Whether you use a T568A or T568B patch cable will not matter as "electrons are colorblind"...as long as the pinouts on both ends are the same, either will work. Make sure to maintain your network standard (Cat.5e or Cat.6). If you use any Cat.5e items on a Cat.6 network, you will lower all your metrics to that Cat.5e standard. As long as your patch cable ends are pinned-out the same (straight through) to either the T568A or the T568B pinout, you will be okay.
A "crossover" patch cable is pinned-out to T568A at one end, and to T568B at the other end. They are (or were) typically used when cascading two or more network hubs or switches. The advent of "smart switches" has pretty much negated their use.