I guess it should work as the AC supply power adapter for the Tab gives 5.3v at 2.00 amps, whereas the DC supply charger is rated at 5.0 volts 3.1 amps ....one for ipads & Tablets at 2.1 amps and one for smart phones at 1.0 amps.
However, I will not use the Tab power supply adapter to charge the S4 Active!
I am hoping that actual users will respond to ease any fears!!