==>As you have mentioned in your design external mux is provided. External mux is used to bypass the PLL clock & test clock will be provided to the design. For transition you have to use PLL clock for capture. For stuck-at you can use test clock.
==>Ensure the model is flop or latch. S1 indicates that whether DFTA is able to change the sequential cell to scannable one
==>Since u have got around 7000 violataions try to put a mux in the downstream(Upper level hierarchy) to resolve s1. Don't let the tool to put the muxes.