Signal Generator output voltage
There can be two problems:

You don't really know what the signal generator output voltage is supposed to be.  You said it is "12v".  You apparently mean 12 V, but is that RMS, peak, peak to peak, or something else?  Until you know that, you don't know what a perfect meter is supposed to read.

Some meters deliberately reject power line frequencies.  Most that do this only reject the 50 or 60 Hz when it is below some percentage of the overall.  I've never heard of a FeelTech.  Check its datasheet.



Let's see what RMS results from a peak or p-p voltage specification.  A sine with 12 V peak is 8.5 V RMS.  12 V peak to peak would be half that, or 4.2 V RMS.  Considering your vague 12 V spec, a 4.2 V reading from a good meter is a possibility.