This thread is interesting in the fact that many of the responders say how fast they run through their tanks, while in other threads some people claim that their tanks (especially BW) lasts weeks. I was always amazed at those people because based on my rate of usage I have to wonder how they use their rigs. So this is where all the other folk hang out. :)
In my case we have 37 gal. BW and GW tanks and can get through a 2 night camping trip without dumping grey. As for BW ... that lasts about 5 days before it is full. That includes doing the dishes for 3 regular meals and taking quick showers. There are two of us.
To the OP's question - looks strange for his 15 gallon tank. I would not suspect the sensors on a new tank, besides he confirmed that the tank is full since he physically checks it is so. I used to have a Jayco HTT and it had 20 gal tanks which were just too small. Had to make sure that we started dumping grey into the black tank just to make sure we can get through a 2 night trip. So with a 15 gallon tank, I am not too surprised. Perhaps some water could be saved doing the dishes but even that sounds optimized. Some folk use paper plates to cut down on the dishes and that could be an option. In summary, his problem sounds like a combination of small tank with a need for more optimization on water usage. Just my 2 cents