Multiobjective with single objectives that use distinct components of input vec? What does it mean for other components in input vec?

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Multiobjective with single objectives that use distinct components of input vec? What does it mean for other components in input vec?

E.g.

$$\min (x_1,x_2)$$ $$x \in \mathbb{R}^2, x_1,x_2\geq0$$

Then if one solves this by one objective at a time, then one solves first $x_1$ then $x_2$. However, the input vector to this problem is $x \in \mathbb{R}^2$.

One could e.g. use initial guess $(0.5,0.5)$. Then the algorithm (e.g. minimize in scipy) might spit out $(0.0, 0.43)$. Since we were minimizing the first objective $x_1$, then the solution that we're interested in is $0.0$. However, the algorithm has clearly varied the second component as well, ending to $0.43$ due to some things in the algo.

Is the $0.43$ redundant? Why is it altered by e.g. scipy's minimize, even when the 1st objective doesn't contain it.