Controlling and induction coil with a SSR

Yes that is exactly what will happen.

This is because the current and voltage are 90 degrees out of phase with each other. So that when the current drops below the holding threshold the voltage has not dropped below the voltage threshold, and a quarter of a cycle later the reverse happens.

You need some phase angle correction on your inductive load to bring the current and voltage waveforms in phase.

That eBay advert is just for conventional resistive heater elements, not induction systems.