The charging plate and the phone are totally two independent systems. The charging plate has no knowledge of the phone and apps running on the phone. If fact the charging plate can be used with other Qi compatible devices.
I have found the battery indicator an estimate of the charge left on the phone and not 100% accurate reflection since the software on the phone only trys to determine how much power is left in the battery.
I would not worry about the the charge light being on even though the phone is showing otherwise, the light is the best indicator that the battery has fully charged or not, as it will detect no more current is able to pass through the battery and auto switch off, as I have had this happen to me too. The light indicator turns off approx 30-40 mins after the phone indicator has stopped flashing.
When I first got my lumia I used it until the battery was totally dead i.e unable to switch it on. I found even when it auto switches off 'Goodbye' message I was able to switch the phone back on after 30mins and it would last for about another 1hr. I then fully placed the phone on the charge plate, it will auto switch off and on several times as the phone battery is starting from zero power and will take 2-3 mins to wake. I then leave it to charge until the charge light turns off.
I repeated this process several times, and found battery life greatly improved. I am guessing a complete drain of the battery and 100% charge and repeating this 2-3 times somehow refreshes the 'internal battery charge memory' and 'primes' all of the charging cells.
I am getting consistent 35hrs between charges (light and moderate usage, no background apps apart from Nokia drive)