Hi wiks,
First winding is "main winding" and the second is "auxiliary winding". Auxiliary winding is only for start-up. If you reverse the current flow of only one winding (main or auxiliary), the rotation is reversed.
there is no need to rectification the source. in this relay, there is a shade pole (a copper ring) as same in shaded-pole induction machine which is located in relay core. This ring eliminate the vibration when ac sinusoid goes to zero.
