If you are flying on your own and this happens accidentally, don't necessarily
expect to notice the crossover. Pilots have spun into the ground thinking they are holding anti-spin controls, when in fact they've crossed over and are holding pro-spin controls. The stress and confusion of an accidental encounter, combined with inexperience may cause the change in yaw direction to go unnoticed by the pilot, since the airplane continues to roll in the same direction, which can dominate your attention.
Of course, if you've had training and are comfortable with inverted spins,
intentionally crossing over is no big deal, since you're now in a regular inverted spin, which you already have experience recovering. When it happens, the yaw will hesitate for a moment before continuing in the opposite (from the pilot's perspective) direction. Roll will continue in the same direction. If you saw it from ground, it would not appear to change direction at all.
My only suggestion when trying it for the first time is to pay special attention to the yaw, and take note of what it looks like when it's reversed. It's best to learn the sight picture and be able to apply the correct input based on what you now see rather than attempting to think back to how you got there, and react based on that alone.
REMEMBER which way you re-entered a spin so your next input is correct. IT's VERY easy to get confused when you go over....
This might be OK if you're doing intentional crossovers, but in a true emergency spin recovery situation where you're likely stessed and a bit confused, most aerobatic airplanes do not even require you to figure out the situation beyond the fact that you're no longer in control. If you spin accidentally, and are confused by what's now happening (or why it's not stopping) it can be best to NOT try to figure out which rudder to push and whether to bring the stick forward or aft. Simply pulling power off and visually neutralizing elevator, ailerons, and rudder will recover most types. It works every time in a Pitts, in any spin mode. I don't have experience in the Decathlon with this method, but have been told it's effective in it as well.