is there like a diagnostic checking(like those in the time series) done for logistic regression and complementary loglog model?
Yes, there are many diagnostic checks done in these situations. Any textbook on generalized linear models should introduce them to you. A lot of them are adaptions of those used in the linear regression case eg plotting residuals to see if they have the distribution expected in the model; plotting residuals against explanatory variables or candidate explanatory variables to see if there is structure that is not explained by the model; etc. Checking for autocorrelation in the residuals would certainly be one thing that should be done if they are a time series.