I guess you have the System 3 alarm fitted??
If you do then the movement sensor is fitted inside the alarm casing itself.
There is no adjustment as such, but you can reduce it by backing off the mounting screws a little. If the unit is screwed down too tight then the sensitivity will be feather touch, as you are finding.
If the unit has been cable tied to your bike, cut the ties, put some foam between the alarm and the mounting point and re tie.
Not very technical, I know, but that is the "approved" method
There is no time limit as such before the alarm goes off. Light movements will trigger a "warning". 50 of these little beeps and the thing goes off.
If there is a big movement, it'll go straight into siren. If the sensitivity is as light as you suggest, you would get many of the warnings.
A way around it, rather than a solution though, is to drop it in "ferry mode" for general parking purposes. Press the oval/triangle button, once the unit has armed and it'll disable the movement sensor. The bike will still be immobalised and protected from hot wiring etc.