That is correct about the charging rates. 0.5C-1C is the right range to be looking at for all Li-Ion cells, with 0.7C the ideal. Exceeding 1.0C will risk over-heating and damage. Charging to 4.1V will extend the cycle life of a cell, as you say.
There are 2 things to look for in the charger. First, is it charging with the correct CC/CV algorithm? With most, this is unlikely, and with cheap chargers like this one, almost certainly not. If it is not using the correct algorithm, termination at the correct voltage could be a hit-and-miss affair. Second, and more important, look at the charge rate. On the back of the charger this should be stated in mA (milliamps). See what I say below about "C", and how it governs charging rates.
I don't know either of those chargers, but the rule is that if the charge rate exceeds 1C for the cell, it is not suitable.
For those who are not clear what "C" is, the long-winded version is that it is the current in miiliamps at which the cell will discharge from full to empty in 1 hour. The short version is very much simpler. Cells have a capacity rating, stated in mAh. For a 10180 cell, the figure is 90 mAh. That same figure expressed in mA (without the "h") is 1C for that cell. Therefore 1C for a 10180 is 90 mA, whereas 1C for a 18650 is 2,200-2,600 mA (depending on the rated capacity of the cell). This is why unless you get a hobby charger, you can't use the same charger for all cells. A charger that charged a 18650 at 1C would force-charge a 10180 at >20C, which would be very likely indeed to cause an explosion. At the other extreme, a charger suitable for a 10180 might take >24 hours to charge a 18650!
So – to see if a charger is OK for a particular size of Li-Ion cell, look at the charge rate (in mA) printed on the charger. If that figure is larger than the mAh capacity of your cell, it is NOT suitable.
To take your example here, the 100 mA stated for the Belkin is ~1.1C for a 10180, which is just over the recommended maximum limit. I'm not exactly going to tell you that it is OK to use it, but I would say that if you kept a careful eye on it during charging, watching and checking for any signs of the cell over-heating, it would be pretty unlikely to cause a problem in a healthy call that had never been over-discharged. As the cell aged, you would notice it heating up a bit more during charging, a sign that it was struggling a little.