a few interesting things, here...one, that you only initially drained 300ml of coolant out on the change, could be the prior owner didn't fill up the coolant all the way, or you have a leak? Filling coolant is not a fast 'dump it in and go' process..if you do that you can trap a lot of air in the system, possibly what your previous owner did?
The other odd thing is the Kymco manual stating to refill the coolant system through the overflow tank. While that is possible in theory, when finished you'd end up with an overflow tank way overfilled. That's not a good thing.
The usual way is to drain the coolant then refill through the filler neck and then fill the overflow tank. The overflow tank's purpose is to provide additional coolant to the system should it be needed (system is underpressurized) and to accept overflow coolant from the system if it's over pressurized. That's why overflow tanks have markings on them for minimum and maximum coolant level. Back in the bad old days the extra coolant would just vent onto the ground...