I've purchased the “Sync Timecode PRO” module on one iOS device, do I have to buy it again on my other iOS device?

You don't need to pay again.

Just make sure that you're using the same iTunes account on your iOS device that you used when originally purchasing the module on your other iOS device. Go through the purchase process within MovieSlate on your other iOS device. At one point (very late in the process), the App Store will ask you to confirm that you want to "download again for free". Just answer yes and this will install the PRO module on your other iOS device.

You must go through the above procedure because syncing the devices with iTunes after purchasing the module DOES NOT enable the module on the second device (although that would be a nice feature for Apple to add to iTunes).