PF starts first engine, sets mode selector to normal and turns APU bleed off. PM then switches yellow electric pump on and completes the after start flow.
ENG 2 start is supplementary procedure by PM with confirmation ONLY required for the engine master switch. PF should be concentrating entirely on driving the aircraft. Even if PM gets the procedure entirely wrong they won't harm anyone or damage anything provided they don't operate a guarded switch.
After engine 2 start normal procedures resume. Not difficult...