Okay, I'm rehashing a 3-year-old argument here, but the rule is that bonus damage expressed as dice is not multiplied on a critical hit, but other bonus damage is. Whether or not it's precision damage has nothing to do with it.
I don't really object to making an exception. But it should probably say "Unlike other bonus dice of damage above and beyond a weapon's base damage, the extra damage from this ability is multiplied on a critical hit."
You can keep the bit about it not being revision damage if you like. People would tend to assume it is, and there are lots of restrictions on precision damage.
If you want create an ability that also allows sneak attacks and such to be multiplied on a critical hit, you could model it after the "burst" weapon abilities.
Prerequisite: Sneak attack, sudden strike, or skirmish class feature.
Benefit: When you score a critical hit when using sneak attack, sudden strike, or skirmish, you deal even more damage. For each extra +1d6 damage the ability normally adds, you add an additional +1d10 on a critical hit. If the weapon's critical multiplier is x3, the extra damage is instead +2d10 per +1d6 the ability normally adds. If the weapon's critical multiplier is x4, the extra damage is instead +3d10 per +1d6 the ability normally adds. (And so on, for higher critical multipliers.)
Normal: The extra damage from sneak attack, sudden strike, and skirmish is not improved on a critical hit.
Special: This extra damage does not apply to any creature that is immune to the base ability (sneak attack, sudden strike, or skirmish), unless you have some means of bypassing that immunity. Likewise, creatures immune to extra damage from critical hits do not take this extra damage either, unless you have some means of bypassing their immunity to critical hits.