1. The hydrazine tank is allegedly likely to survive re-entry intact (being thick to hold the pressurized material, as well as insulated and surrounded by the rest of the satellite). Thus it could survive to burst on impact, releasing the fuel at ground level.
2. The SM-3 missiles are the same as those used for theater & re-entry-phase ballistic-missile interception.
3. At the altitude, speed, & flight path that will exist at the time of the shootdown attempt(s), the satellite will be acting much like a missile beginning re-entry (with a few extra zigs & zags).
4. The maximum range of the PAC-3 is nowhere close to what will be needed here.
"The goal is to hit the satellite at about 130 nautical miles away from the Earth."
What I have seen for the PAC-3 lists a max missile-intercept range of 45km, and a max altitude of 15km.