It's more likely that either the data is just going fast enough to give you that impression...or that your steady state, i.e no data transferring, has the same sense as you have your LEDs connected in...so if the steady state is high on both pins, arrange it so that the LED anode is to Vdd, cathode to tx/rx but if the steady state is low, then arrange the LEDs with the cathode to Vss and anode to Vdd. Obviously you require current limiting resistors on both LEDs.
A better way would be to use a tricolour LED and a couple of other port pins if you have them spare. Set each one on whenever there was data in either the receive buffer or transmit buffer, and switch them off again when the buffers were empty...that way you will know at a glance whether data is flowing and in which direction or both directions etc by the colour of the LED...