Assemble should only be used when placing a component from the Place Component dialog (it was poorly implemented and not clear to end users at is conception), its pretty useless as a normal relationship tool. In fact it was moved to the expanded panel in Inventor 2014 and 2015.
Learn Insert constraints instead of axial mates. But if you must use one and need to flip, it helps to use the Rotate Component command to rotate it first.
Inventor can't back-calculate the result when you have constrained a part to all three axes and then decide one is backwards. Even though there IS a solution, Inventor can't find it. What you can do is suppress one of the other two, correct the one you want to reverse, and then un-suppress the second one.
Later as you learn, you will discover the uses for suppressing constraints so this is as good a time as any to go looking for that (in the feature tree, right-click on the constraint listed under the part in question).
To have more control over the position of the part when it is constrained, I avoid axis constraints, exactly because I can't control the orientation. When constraining to planes, I can select "mate" or "flush" which allows orientation relative to the positive normal direction of the plane. Not so with axes. They don't always have an obvious positive direction.