The simple answer to your question is No, it doesn't mean apnea. The monitor attempts to detect movement, and it goes off when it does not detect movement. The slight breaths of an infant could easily be missed by such a device, which consists of a pad beneath a sheet beneath your clothed child.
The American Academy of Pediatrics specifically recommends against these monitors (here as well). They have not been found to reduce the incidence of SIDS. If your child is at risk for SIDS, your pediatrician will arrange for a proper apnea monitor which uses electrodes attached to baby's tummy rather than a mat beneath the baby's sheet.
Products such as these seem to prey on the fears of new parents. You are afraid to sleep because something could happen to your child while you are sleeping. This is understandable. Welcome to parenting! Every age and stage will bring new fears, and you must learn to deal with them, not by building in a false sense of security by avoiding every possible risk, but by accepting that fear is part of the job you have signed up for! The longer you do it, the better you become at it, but the fear will never completely go away. It's part of what makes parenting such a rich experience - you love your child so much that your are prepared to live with the fear that comes with his learning to take risks in the world. The first such risk - sleeping alone.
Still unconvinced? Think about this - The use of such a monitor means every time your child gets into a deep enough sleep that his movements are not detected for 10 seconds (and I will tell you that proper apnea monitors are not usually set that low!), the monitor wakes him up with a vibration. What quality of sleep is your child getting? At 20 seconds, the whole house is awoken - bad sleep all around.
To reduce the risk of SIDS, you are much better to follow the other recommendations of the AAP (see link above), like breastfeeding if possible, getting immunizations, not using bumper pads, sleeping baby on his back on a firm surface (though baby will eventually choose his own position). Also, be sure to give your baby tummy time when awake, as this will prevent "flathead" and help develop neck muscles which will allow the baby to adjust his own head position when blankets or other materials are impairing his breathing.