This is patent (US 4,202,133) from May 1980 that had a similar goal but I doubt it worked. It's from Raphael Sahar of Tiberias, Israel.
The propeller on top is optional. The axle 11 is fixed to the top and would rotate it's body. From the description: "It is the object of the present invention to provide a spinning top which . . . spins automatically on hitting the ground (or any other surface) when dropped from above."
As you can see, it has a ball attached to an axle with a spring, and when pushed in engages some pinions and gears. It's not clear on the drawing, but there are ratched mechanisms (12) so the gears don't spin backwards when the axle extends out.
I doubt that the inventor ever built a prototype.
There is no mention on the patent of the required friction between the ball and the bouncing surface without which the tip will just spin backwards and no net momentum would be generated.
There is a continuation patent (4,233,774) where the axle goes threw the body and just spins a propeller, which supposedly would be enough to make the top fly. The patent doesn't say it, but I guess the top would have to be spun by other means.
Four years latter, the same inventor put a motor inside the top to rotate the propeller and the spring tip only serves as a switch to temporarily turn it on each time it hits the ground (US4,453,342).
I'm curious to see if the Ta-tack has a way of disengaging the axle (friction plate, ratchet, one-way bearing) for the back stroke or if just extends when it's in the air.