I could not find the above quote in your link page. However, the datasheet does NOT mention a post-charge "trickle charge mode". The datasheet implies that once the battery voltage hits 4.20V (adjustable but this is the default) it will enter a "constant voltage mode", and then implies that it will charge as needed to maintain that voltage. I could not determine, from a quick search, what threshold will trigger a charge.
ETA: On a second read, it appears that a "trickle charge" cycle kicks in again when the battery voltage drops to between 94 and 96.5% of the target voltage (4.2V), or roughly 3.99V.
I think we have a definition problem here. A typical NiMH charger will fast charge until a predetermined cutoff point, and thereafter will apply a constant current to the battery, continuously and forever. It is a very "dumb" mode that keeps the battery fully charged. This is at least my interpretation of the meaning of a "trickle charge mode".
What your quote suggests, in combination with the rather vague discussion I found in the datasheet, is a much smarter mode that will periodically restart a charge cycle and then shut it off when the battery voltage drops below some threshold value. It is not a dumb but low current continuous charge mode.
According to batteryuniversity.com, based on actual real world tests they reference, the optimum point to recharge a Li-ion is about 50% charge. Recharging after a complete or near complete discharge results in somewhat less battery life, based on full charge equivalents. Similarly, and very importantly here, they also indicated that recharging at a 90% charge level would result in about the same effective battery life as a full discharge. That suggests that leaving a battery in a charger with such a constant voltage mode full time, essentially forever, would very modestly reduce the useful life of the battery.
But that is not the issue here. It was suggested previously here that batteries should be removed from the charger "as soon as possible" after charging completes, and it was that suggestion that I addressed. That "as soon as possible" suggestion also implied related safety issues but I don't think that can be substantiated by anything in the charger datasheets or other credible information. It is merely a matter of how to optimize battery life. I don;t think leaving a battery in the charger for a few hours, or even overnight, is going to trigger so many constant voltage recharge cycles to have much effect even on the battery life. These batteries don't self-discharge all that quickly, unlike standard NiMH batteries for example.