Depending on the watts you are vaping at, that could explain the mod cutting off early. If you are drawing enough power that it drops them below the cutoff voltage under load, some mods will cut off(which I think is a good thing). As for the charging, that isn't really that unusual. Most chargers say they will charge to "4.2v +/- 1%" That 1% would be 0.042 volts. Let's just use 0.04 to make it easy. To get a lithium cell to a resting voltage of 4.2v, it will have to be charged to slightly over 4.2v while on the charger. This can start to get dangerous. If a charger stops charging at 4.2v, the resting voltage may be around 4.15 volts(mine are always 4.15 or 4.16 when they come off the charger). Now, when you figure in the 4.2 +/- 1%, if the charger is only charging to 4.18v and they drop down a little when they come off the charger, seeing 4.13 as the resting voltage is easily within the realm of possible. These numbers also assume that the charger and the multimeter you are using to read them are perfectly accurate. Most multimeters are +/- 0.5%. When you add in the range on the multimeter, seeing 4.13v after popping them off the charger is totally possible. I wouldn't be concerned about that. I also wouldn't be too concerned about them coming out of the device when they are at 3.46v if you are running at higher wattages. This could be the slight inaccuracy of the board in the mod.
All that being said, if you are concerned about it, I wouldn't hesitate to contact the seller you purchased it from. It never hurts to ask.