That's probably correct; automatic activation of Unlimited Turns generally occurs only at the time of purchase and only on the device used to make the purchase*. You can use the feature on your other devices that use the same app market without paying again. To do so, please follow the instructions on this page.
*The exception to this is Kindle Fire players using WhisperSync. If the state saved in the cloud included Unlimited Turns, the Unlimited Turns will appear when WhisperSync retrieves this state from the cloud. In other cases (e.g., if the state saved in the cloud does not include Unlimited Turns), you should do the manual activation.