You are configuring the NPN transistor as a common-emitter amplifier, which has voltage gain, will saturate, dissipating minimal power, and fully power the relay.
You are configuring the PNP transistor as a emitter-follower amplifier, which does not have voltage gain, will never saturate, dissipating excess power, and not fully power the relay.
It might work, but not optimum with the same components. If you change the PNP to a common-emitter configuration, it will work as the proper compliment to the NPN.
Or drop the two transistor, two resistors, two SPDT relays (and diodes)...and drive a DPDT relay (w/diode) directly off of the 555. Assuming the 555 can handle the relays coil current. If not, add the NPN and resistor back in.
Ken