Example 1. Interior and base browning/dieback.

Here is a link that might be useful: base and interior

Brown tips

Here is a link that might be useful: brown tips

Insecticidal soap can easily burn foliage, especially of conifers, and especially if applied during the summer or on a sunny day. If the browning and dieback you observe occured after application, then that might be the cause.

They say it helps to apply in the early morning or evening, then wash it off with water after 15 min. It doesn't take long to kill the little buggers.

Alex

Very difficult to tell from photos. Did you actually see spider mites? You can usually see them by shaking foliage over a white sheet of paper.

A common disease on many Cupressaceae during moist, warm weather in the SE is Cercosporidium foliar blight. However, your photos are not enough for diagnosis.