Q1 has its base on DTR through R1 and its emitter on RTS; its collector pulls EN. Q2 is the mirror image: base on RTS through R2, emitter on DTR, collector on IO0. A transistor conducts only when its base side is high and its emitter side is low:
DTR = 1, RTS = 1: both transistors off, EN = 1, IO0 = 1.
DTR = 0, RTS = 0: both transistors off, EN = 1, IO0 = 1.
DTR = 1, RTS = 0: Q1 on, EN = 0 (chip in reset), IO0 = 1.
DTR = 0, RTS = 1: Q2 on, EN = 1, IO0 = 0.
Because equal levels switch nothing, opening a port that asserts both lines together does not reset the chip. When a transistor is off with its emitter high and its base low, its base-emitter junction is reverse-biased by 3.3 V, well inside the 6 V minimum V(BR)EBO of the 2N3904.