Statistically Significant Covariant in MANCOVA- Next steps?

Good afternoon,

After settling on MANCOVA (or at least the Multivariate GLM option on SPSS) I am confused by the results.
Some significance was found between my dependent and independent variables- but also significance for my covariates.
There was even a case of no significance between variables, yet a significant covariate.

What steps are needed to adjust the MANCOVA to appropriately account for the covariates?
Or am I misreading it and the MANCOVA automatically adjusts for it-
As in, is it reporting what could have interfered, and I go ahead and present significant findings?
Why do you care about the statistical significance of covariates? Ususally ,covariates are included to adjust for confounders or to reduce error variance, but they are not of substantial interest (in which case they would be introduced and discussed as predictors, in my opinion).