Did you measure at A above middle-C? (A4) The Cleartune app may not take the inharmonicity of your piano into account. Depending on how far away from that reference it is measured, you may see confusing results.
When I installed the professional tuning software called Tunelab on my iPhone and iPod Touch, it did not need calibration at all on either device when compared to the NIST analog standard. Spot-on, to the accuracy allowed by the calibration function of the software. I do not know if this is typical, but I suspect there is not that much variation between devices, at least not enough to be off by 15-cents at A4 (about 4 Hz).
Was there direct sunlight on the piano when you measured it? A tuner should call out environmental conditions that may affect your tuning stability. Temperature change is one way to get very rapid instability on your tuning.
A possible reason for "floating" pitch, since you say it is tuned twice a year, is if your piano has a relatively wide natural variation in pitch from low to high humidity seasons. Depending on the particular time of year, a tuner may not watch to "chase" the pitch up and down with the seasons. In this situation, I would try to recommend the best time of year to tune such that a piano would be close to pitch for as long as possible.
There are many variables, I would definitely ask your tuner what his intent was, describe how you took the measurements, and see what his response is.