I put freshly charged 2200 mAh battery (SBR-14LI) the one that comes with the FT3DR on the radio. I then plugged in the AC adapter and connected it to the radio. The "Now Charging" text came on with a bar on the screen. I watched over it for a few minutes and it remained the same. I then walked away for about 15-20 minutes and when I returned the display was off. Per the manual, when the charge is complete the radio turns off after 3 minutes. Based on that my radio and battery appear to be working normally. The manual also notes that it takes about 9 hours to charge the battery, perhaps more depending on the status. (Page 20)
While your radio shows a full battery when you turn it on, I wonder if it is really topped up. Leave it plugged in and turned off and when if it still says "Now Charging" tomorrow, there may be an issue...or not. Honestly, if you have left it charging for 8 hours and it shows a full battery when you turn it on, I would think it is working okay. You can of course contact Yaesu and ask them. There are not any firmware updates for the FT3DR radio at this time, so what we have is the latest.
I think I charged my FT1DR radio once or twice with the AC charger and it took too long for me. I purchased an extra battery and drop in charger, which I then used the the FT2 and FT3.