jbm had some great points. As did a few others. I see that this post is an old one, but the question does come up frequently. So here's my 2 cents (no pun intended).
First, nice piano. Second, always talk to your tuner immediately upon discovering any topic of concern. The sooner, the better. Then my recommendation is to get a temperature and humidity gauge that records minimum and maximum levels for both. Then place it on the piano and observe the results over the following days, weeks, months and seasons. The more stable the temperature and humidity in and around the piano, the more stable the tuning will be and the better for the piano over all.
A quick qualifier about myself. I am the 5th generation in a 6 generation piano business. I have personally rebuilt, restored, repaired, or tuned hundreds of pianos and have been responsible for thousands more. I have been using a computer controlled tuning instrument for over 25 years. It creates a custom stretch tuning for each piano, taking into consideration that pianos unique inharmonicity. So I feel that I know something about computer aided piano tuning.
Back to your question. One (1) Hertz (aka cycles per second) equals 4 cents. Concert pitch of A-440 is simply means three strings at A4 vibrating in unison at 440 cycles per second - period. Doesn't matter if it's summer or winter; an aural (by ear) tuning or a computer aided tuning ... A-440 is A-440.
One hundred (100) cents constitutes a semitone, also known as a half-tone or half-step. Therefore, A4 to A#4 is a semitone or 100 cents (¢). In your example of 15¢ flat (15/4= 3.75 Hertz flat) your piano was at A-436.25 (when you measured it) or 0.852273% flat. If you live in the northeast, seasonal changes will produce greater changes in pitch than that. You would be doing a pitch raising in the winter and pitch lowering in the summer; changing the pressure within the piano by thousands of pounds each time. To put it into perspective, a concert piano is tuned before every concert. We include 4 tunings and an action regulation check during the first year. We install a humidifying/dehumidfing system with a humidistatic control when we are commissioned to do a restoration or rebuild - that is how important humidity control and maintenance is to us and the piano. If your piano is near a window, door, fireplace, air conditioner, etc. you will have frequent pitch changes making getting a solid, long-lasting, right on pitch tuning next to impossible.
Regarding informing the customer of the pianos condition. Before we even book a tuning for a new customer, we ask several questions. Such as: is the piano played with other instruments (or voice)? What is your piano playing skill level? Does any one else ever play it? When was it last tuned? How old is the piano? Plus many others. The point is, we try to gauge.their needs and expectations and discuss them BEFORE we even book the tuning. Discussing a pianos condition too much while at the house usually doesn't turn-out very well. Just telling someone that a piano should be tuned 4 times the first year (if new), twice a year thereafter and the action regulated every 5 years can be a big turn-off. When was the last time someone checked your plate screws for tightness, set the strings on the bridges, spaced the strings, filed & voiced the hammers? How often have you heard that you should tune a piano at least once-a-year? Especially if it's not being used! Once-a-year tuning is an insurance policy to protect your investment and minimize long-term damage to the piano. If three piano is not worth tuning one a year, sell it. I can not remember how many pianos have be ruined by lack of service. I can remember the few that were destroyed by abuse. I hope that this is helpful to future readers of your post.
