Yes, all animations are relative to the bind pose. This is just as they are in Spine, where animations in animate mode are relative to the bind pose in setup mode. This makes for a lot better workflow in the editor, and also allows the bind pose to be manipulated at runtime and all the animations will be affected, eg to lean forward while running up a hill.
If the export had an option to combine the bind pose with the animations, then it would be expected that runtimes can support this alternate format. Current runtimes apply the bind pose at runtime, which is the more flexible of the two approaches. If your runtime doesn't want to do this, you could combine the bind pose with animation data at load time or write a tool that converts from the Spine export format to your own format. Are either of these acceptable?