Trainer & Road bike

Magnet measures how many turns your rear wheel has made during your ride, and calculates according to the diameter of the wheel to get the total distance.  THen according to how long you have been riding, it calculates your speed.  So it should be pretty accurate mathmatically. 
However.... riding on a trainer is very different from riding on the road.  I tend to ride a lot "slower" on the trainer. 
Some trainer allows you to adjust the friction of the rotar - less friction = easier = faster.  But it does not resemble real road conditions. 

When you set up the computer, make sure you input the diameter correctly - most computer defaults to the 700C wheel which is pretty standard for road bikes (unless you are a smaller person and use the 650 wheel, it is written on your wheel/tires). 

It should work if the magnet and the pickup are on the rear wheel.  This also assumes the correct coefficient is programmed into the computer for that wheel size.

One way to check -
1.  determine which gears (front and back) you're using while on the trainer
2.  determine your cadence (count the number of times your left leg comes up for one minute)
3.  use the calculator at Sheldon Brown's website to determine speed for the gear ratio & cadence.  Link

I recently went out with a buddy for a ride, he has a cycle computer fitted with the sensor on the rear wheel, after we had covered around 12 miles the cycle computer had us at 2 miles, adjusting the magnet slightly then had us covering 26MPH for the next section, which would be nice but it was all up hill, and neither of us are actually that good, in fact not close :-)

So there can definately be issues with the readings you get, I guess maybe quality of product, battery state in the sensor and head unit, his was a wireless one, so perhaps issues there due to low batteries, but for sure you can get some odd readings.