@Rtjs Do not use the plug converter, simply plugging your original Rachio power adapter will fry your new controller. The type of transformer used within the AC converters, such as the one used by Rachio, is really a step down converter, with a fixed ratio of 4.4 to 1 (in order to convert 110VAC to ~25VAC), plugging it into the 220V source would step it down by the same factor of 4.4, thus outputting 220 / 4.4 = 50 Volts AC. Such overvoltage would likely fry the surge protector.
It is possible to find a 2 to 1 step down transformer to convert 220V to 110V in order to use the original Rachio transformer, but few of those devices are designed to be used 24/7, for best results you would want to seek a 220V to 24VAC adapter, such as the one found by @FosseVet:
During your search, be careful to avoid adapters that output a DC (direct current) voltage. Be sure that you see 24VAC as output rating, with power rating going not much higher than 1000mA, 1Amp or 24VA.
TLDR: Frequency is not an issue, proper output voltage is. Orignal plug cannot be used with 220V, you need to avoid a DC supplies when searching for a replacement.