My Sony laptop was the
only battery device I got that had instructions that matched battery type. I don't know what brand my sister's laptop is but it had instructions suitable for Nicad.
2 electric shavers, Lion and NiMh both had the same charging instructions for Nicad. And then there's the e-cigs.
Odds are the Li-ion charger is doing nothing once it turns green, if it does something you'll see it cycle to red just like you may see it cycle to green while it's charging.
A trickle would be bad and I don't think a new Li-ion should be losing enough charge to kick the charger on in 8 hours.
I wouldn't worry about overcharging. Hopefully the people who design the chargers actually know about batteries, they just make too much money to write the manuals