(or, Q: Does TextExpander transmit all my keystrokes to Smile's servers? A: No.)
TextExpander touch 3's custom keyboard requires Full Access to function as you'd expect a keyboard to, and the warning iOS presents about this is quite ominous:
The TextExpander keyboard needs to share snippet data with the TextExpander app and to play sounds, such as key clicks and the expansion sound. These are only possible if Full Access is turned on. The TextExpander keyboard does not transmit your data on any network, Wi-Fi or cellular. The keyboard maintains a small buffer of recent key taps for the purpose of matching a snippet abbreviation. The buffer clears after a limited number of key taps, and is never saved to a file or transmitted anywhere. The contents of the buffer are neither stored nor shared with the TextExpander touch app.
Without Full Access, keyboards operate in their own container, which means they don't have access to data from other apps, including the TextExpander app itself. It also means they have more limited access to system services, for example, they can't play sounds. Once a keyboard is granted Full Access, it can share data with another app from the same developer. Once it can do that, the other app can do pretty much anything with that data, including transmitting it over the network. Simply because an app CAN do this doesn't mean that it DOES, nor that it's wise of the app's developer to even consider doing so.
Any standard app on iOS can store and transmit your keystrokes, and this has been true long before iOS 8. Apps in general don't do this because it would be a severe abuse of your trust. Any app caught doing this without your permission would at least be panned on the App Store, if not removed from sale by Apple.
What's new in iOS 8 is that extensions can be more severely limited than apps. This is a great way for new app developers to build trust with users. For established app developers, it can be too limiting, and that's certainly the case with TextExpander. We have done our best to earn your trust over the past 8 years of TextExpander for OS X and 5 years of TextExpander touch for iOS. We tell you what we do with Full Access, and we tell you what we don't do, then we match that with our keyboard's actions.
It's fair of Apple to warn users of the extent of what Full Access means. It’s up to keyboard developers to make the case for Full Access to their users. Perhaps, in a future iOS update, Apple will allow space for a timely message from developers about their keyboard's specific needs for Full Access. For now, we have Apple's accurate and all-encompassing warning to keep users installing keyboards with a healthy sense of caution.