This tachometer works. It is what it is and it does what it does. It has three modes: off, 2-blades, and 3-blades.
What it does is count blades casting shadows on its top photodetector. Its sampling period is one second and it measures N blade-shadows (b-s) in that one second, where N is a nonnegative integer. The lowest nonzero b-s count is 1.
In 2-blade mode, if it detects 1 b-s in a sampling period, it will report 30RPM (think about it). Do not use 3-blade mode, it adds nothing for fan monitoring. Just consider it takes two pushes on the mode button to turn the device off, and only one to turn it on.
Your fan has M blades, where M most commonly is 7. If your fan has 7 blades, you must divide the reported RPM by 3.5 to get the true RPM. 1 b-s per sampling period is reported as 30RPM, divide by 3.5 to get the true RPM of 8.57RPM. Since the b-s value is an integer, you should not be surprised that this tachometer provides RPM figures for 7-blade fans that's an integer multiple of 8.57RPM. This means the resolution at 857RPM is about 1%, and at 428RPM about 2%.
These resolution figures are very reasonable for the device's intended use, measuring RPM of model airplane propellors, where RPMs of 5000-10,000 are commonplace.
By comparison, the RPM detector on your computer measures 2 tach pulses per RPM, with a sampling period of ~4.8 seconds. The minimum count per sampling period is one tach pulse, and the minimum nonzero value is ~6.25RPM. The number of blades on your fan does not matter. All RPMs reported by your computer are integer multiples of ~6.25.
Your computer has one additional problem not shared by the $17 tachometer - interrupt latency. The ~4.8 second interrupts arrive very regularly, under control of a computer clock. But the computer has a number of tasks to accomplish each interrupt, and measuring the fan's RPM is not the highest priority. So a variable amount of time elapses from the interrupt to gathering tach pulse samples and the calculation of the new value of the fan's RPM.
Worse, on my K8S-MX mobos (for instance) the CPU fan had a higher interrupt priority than the system fan, so the fluctuation of RPM from one ~4.8 second sampling period to the next was higher for the system fan. This fluctuation could be reduced by reducing the number of active tasks the computer was performing.
On your computer, you can use Speedfan's RPM chart feature to gather a history of the individual sampling-interval RPMs and mentally deduce the average value, hence providing a very accurate RPM figure with much higher resolution than 6.25RPM.
Using the $17 tachometer, you can watch the reported RPMs that are being updated once a second. After a short while - a dozen seconds? - you can get a "feel" for the average RPM. Divide this value, which exists only in your head, by 3.5 (for 7-blade fans) to get a more accurate RPM figure.
I now have both a stroboscope and a tachometer. A stroboscope is both a light (pulse) source and a photo-detector. This means it can easily measure the RPM of an exhaust fan mounted in a computer case. A tachometer has a photodetector but depends upon a light source which must shine through the fan blades before impinging on the photodetector. This is problematic for exhaust fans, especially if they are ducted internally to (for example) a Ninja heatsink. On the other hand, I can buy over a dozen hobby tachometers for what I paid for my stroboscope.
You cannot use the hobby tachometer in the presence of A-C powered lighting. In fact, turning the tachometer on under flourescent lighting and seeing it report 3600RPM is the standard way to functionally test the tachometer. You'll need a penlight with a tight (narrow) beam, or the equivalent.
Bottom line: the tachometer
works, is really cheap, but is not as convenient as a stroboscope costing a dozen times more. You takes yer choice and you pays your money (or not).