There isn't a single standard for how tangent space normal maps are supposed to be interpreted. For games, where they are very popular, this isn't a problem, as assets and code go hand in hand. For other programs, it seems like everyone came up with their own recipe and that makes it hard to interchange normal maps reliably.

For what it's worth, normal maps in SuperFly use the "MikkT" tangent space, which is gaining in popularity and source code for generating those tangents is available to everyone.