Fuse blowing in 12 multimeters rated for 200mA, only measuring 12.5mA. Why?
Fuses blow when excessive current flows through them.

The likelihood of this being a batch-related problem is improbable in my opinion - most fuses are safety-critical components, usually with regulatory agency marking - especially parts rated 250V. 

Can you post a photo of a failed fuse? The metallic end-caps usually have markings indicating ratings, manufacturer and regulatory information.

This issue presents a good opportunity to teach your class how to do methodical troubleshooting.

Try this:


With a good meter, measure the resistor before installing it in series with the power supply.
Wire up your circuit - power supply, the series-connected resistor and a good (one in which the fuse is not blown) series-connected DVM in milliamp range, as per your experimental criteria.
Disconnect the positive power supply connection and measure the resistance between where the positive connection was, and the negative of the power supply. You should see the resistance of the resistor plus the resistance of the shunt inside the DVM (which should be extremely small; perhaps not even visible). If you see some resistance smaller than the resistor value (i.e. zero) something is wrong and you need to check your setup.
Do your Ohm's Law calculation to establish the maximum expected current based on the expected power supply output and the resistance you measured. Also calculate the worst-case current based on the worst-case power supply output.
Connect the positive power supply connection and do your experiment.


If you continue to pop fuses, there are two hypotheses that come to mind:


The power supply output exceeded the worst-case prediction.
The fuse could not handle the worst-case current.


Proving which was the cause is left as an exercise for the students ;)