When you evaluate a LR model, the effect of _any_ independent variable in the model is interpreted as follows:
For each unit change in (this IV), we estimate that the log-odds of cases being in the target outcome group (e.g., 1 instead of 0) increases by B (the regression coefficient) units, when all other IVs in the model are held constant.
Or, for those who love odds or odds ratios:
For each unit change in (this IV), we estimate that odds of cases being in the target outcome group (e.g., 1 instead of 0) increases by exp(B) (the exponentiated value of the regression coefficient) units, when all other IVs in the model are held constant.
In either case, the phrase, "when all other IVs in the model are held constant" implies that, yes, you are "controlling" for the other IV/covariates you have included.