A question about the working principle of a frequency to voltage converter
There are several possible sources of uncertainly and noise in any type of conversion. For this case, there will be error in converting the frequency to a digital value, and additional error in converting the digital value to a voltage.

Frequency to digital

I'm not exactly sure how the device you are using works, but there are a few different ways to make a frequency measurement. Which one is used depends on the application:


Count the number of edges of the input signal occurring during a certain measurement window (gate time).
Using a higher speed clock, count the number of cycles between edges of the input signal. The resolution of this measurement is based on the least significant bit/step size, which is the fast clock period. This could be combined with more specialized analog delay measurements to achieve better resolution. Another way is to calculate the average of multiple such measurements.
Record the voltage vs. time with a relatively high speed ADC, then take an FFT of this data and report the frequency bin with the most power. This is useful if the input either has multiple frequencies combined, or if the input is so noisy that it makes it difficult for the input circuitry to determine the number of edges.


One source of error common to all 3 types is the internal clock (e.g., a crystal). This type of error will probably show up as a temperature-dependent offset below 50 ppm (0.005%). It's probably not the dominant error source in your situation.

The measurement resolution for all 3 types is generally better (smaller) for longer measurement times. Frequency counters sometimes allow you to directly specify the measurement time, but sometimes they calculate the measurement time automatically if you specify the expected measurement range and/or resolution. 

Digital to analog

The digital measurement needs to be converted to an analog voltage. It will first be transformed digitally based on the input/output ranges, then sent to a DAC (digital-to-analog converter). 

The digital transformation is often a simple linear scaling, but for measurements spanning a large range like this one, logarithmic scaling should be used. For example, using a simple linear scaling from [1 Hz, 1 kHz] to [0 V, 10 V], 10 Hz would only show up as a 0.009 V output, which is too small to generate or measure easily. Instead, a logarithmic scaling would equally space the values 1 Hz, 10 Hz, 100 Hz, 1 kHz within the 10 V range, so 10 Hz would be 2.5 V. 

The resolution when using a logarithmic scale will not be a constant. The gain to convert from frequency to voltage will vary with the frequency. Using the example from 1 - 1000 Hz to 0 - 10 V again, the gain at different frequencies is:


Near 1 Hz: 1.4 V / Hz
Near 10 Hz: 0.14 V / Hz
Near 100 Hz: 0.014 V / Hz
Near 1 kHz: 0.0014 V / Hz


The DAC itself will add some voltage inaccuracy/noise to the output. Also, if you are converting it back to a digital value (using a DMM or another microcontroller) that will also have some error.

Conclusion

I don't know exactly how the device you are using works (I didn't read the document), but it's possible that if it simply has a set of input frequency ranges to choose from, these automatically affect both the frequency measurement time and the endpoints of the digital-to-analog scaling function.