I would not leave any lithium batteries unattended while charging. With that said, the red AWs used on the Provari are as stable as lithium batteries come for mods. But nonetheless, you shouldn't leave them while charging. Show them the same level of attention you would if you had a fire in your fireplace...you don't need to watch it every second but you want to keep an eye on it. DON'T CHARGE THEM NEAR YOUR FACE, CHILDREN, OR PETS. If by chance one explodes, they usually start a fire which you would need to extinguish before it becomes an all-out home fire. So if you haven't already, consider a small and accessible fire extinguisher as a good investment. I usually keep one in the same room in which I charge batteries in just in case. A LiPo charging bag will contain an explosion in most cases. I have the Pila...and as safe as it is I still do not leave it unattended.
And as far as leaving them plugged in after charging, this is not a good idea for lithium batteries, as lithium batteries are VERY sensitive to overcharging, where as older traditional rechargeable are not sensitive like the lithium-base ones. Also, lithium batteries lose very little energy from just sitting, unlike NiCad and NiMH batteries. This is where the concept of leaving them plugged into a 'hot' charger came from...but for lithium batteries, leaving them in only risks harming them and not helping them. Depending on your charger, this can also shorten service life greatly. While chargers (and even some battery units) have overcharge protections, these do not always work, as evidenced by the many eGo explosions (or these eGos do not have any protection at all, which is even worse). If you have lithium batteries in which you will store (as in if you keep a few spares for down the road), you should store them at about 50%. Storing at a full charge will shorten service life and storing them empty will kill them.
And as always, anyone who uses rechargeable batteries (or electricity at all for that matter) should own and become competent with using a multimeter. If your charger is charging the batteries beyond 4.22-4.25 Volts-ish, then disgard both the charger and the battery as neither are safe for use on a product you hold inches from your eyes.
