Prediction using brms-fitted model with residual correlation

I’m using brms to run a linear regression model (two variables) with random-effect on time series data( divided into several segments because the characteristic should be different among periods)
When I added “autocor= cor_ar(~time|period))” to the model, it seems that the temporal autocorrelation of residuals is nicely adjusted, but the fitting seems too good for me. ( i used tidybayes::add_fitted_draws)

I’m wondering if
1: the serial correlation of residuals is rightly incorporated in my model using “autocor=…”,
2: there is a nice way to get predictions from each segmented periods