As robot deployments become more commonplace, people are likely to take on the role of supervising robots (i.e., correcting their mistakes) rather than directly teaching them. Prior works on Learning from Corrections (LfC) have relied on three key assumptions to interpret human feedback: (1) people correct the robot only when there is significant task objective divergence; (2) people can accurately predict if a correction is necessary; and (3) people trade off precision and physical effort when giving corrections. In this work, we study how two key factors (robot competency and motion legibility) affect how people provide correction feedback and their implications on these existing assumptions. We conduct a user study ($N=60$) under an LfC setting where participants supervise and correct a robot performing pick-and-place tasks. We find that people are more sensitive to suboptimal behavior by a highly competent robot compared to an incompetent robot when the motions are legible ($p=0.0015$) and predictable ($p=0.0055$). In addition, people also tend to withhold necessary corrections ($p < 0.0001$) when supervising an incompetent robot and are more prone to offering unnecessary ones ($p = 0.0171$) when supervising a highly competent robot. We also find that physical effort positively correlates with correction precision, providing empirical evidence to support this common assumption. We also find that this correlation is significantly weaker for an incompetent robot with legible motions than an incompetent robot with predictable motions ($p = 0.0075$). Our findings offer insights for accounting for competency and legibility when designing robot interaction behaviors and learning task objectives from corrections.