I just tested this because I couldn't get my head around it.
The Activity app should monitor steps, calories, time standing, whether it's connected to a phone or not. When it has a phone in range, the data is mirrored in the Activity app on the phone
The Heart app on the watch syncs to the Health app on the phone
The Workouts app on the Watch syncs saved workouts to the Activity app on the phone and various data points (steps, distance, calories) to the Health app on the phone. This worked for me as advertised
So your experience means something's not working as it should. It may be (I'm speculating here, so don't be astonished if I'm wrong) that the issue is around GPS (yes, I know that's not relevant to tennis 🙂 ). The watch uses the phone's GPS to measure distance *and* to calibrate your stride. So maybe there's an assumption built into the software that at least the first few significant activities will be with the phone in range.
Another possibility, based on a conversation I had with an Apple guy (not an expert) is that these early versions of the apps are built for "steady state" activities, like running, walking, cycling and don't yet handle explosive burst activities, like racket sports.
Not the most satisfactory answer in the world, but I hope it helps