The barrel adjuster does not adjust the cable at all, it changes the effective length of the cable housing that the cable moves in. All the tension that is on the cable is generated by the derailleur cage spring. It is (the barrel) a last fine-tuning adjustment that affects all the shifts in the same way. Its real purpose is to have a way to compensate for stretching in the cable over time.

The chain should be on the biggest cog when adjusting the outboard cage limiter screw of the front derailleur, and on the smallest cog when adjusting the inboard cage limiter screw.