I have a large industrial processing machine, there are a set of heaters out on the machine that occasionally fail. The way these heaters are wired, there is a main feed of 480VAC, 3ph which is fused at 70 amps. Out on the machine at the heaters there are 25 amp Circuit breakers (Curve C) for each leg of the 3 phase.

Why does the main 70 amp fuse blow when the 25 amp breaker trips?

The breaker could have a "shunt trip" installed. This is a heater which will cause the breaker to trip. The heater has to be powered from the load side, so that when it trips voltage is removed from the heater.

Look for 2 smaller terminals attached to the breakers. One can be a switch on the "tripper" and the other can be the "shut trip" on the "trippee". In this case, power is cut from the entire machine when a heater trips.

You have to check the fault level of the beaker & the Fuse the discrimination level should be higher on fuse than breaker .

A shunt trip is not as described. A shunt trip unit in a circuit breaker is actually a coil, much like those found in a magnetic contactor or motor starter, and needs control voltage to operate.

A shunt trip unit can be used to open a breaker remotely, either manually if desired by an Emergency Power Off pushbutton, or automatically, by a monitoring system that can send a signal to the breaker to open for safety purposes.

The heaters described is more like an overload trip unit found in a magnetic motor starter.

I have never heard or seen the word "trippee" used in electrical jargon.

What Jit is referring to is AIC rating, or Available Interrupting Current. I do not believe this is the issue, but Jit is close. AIC rating is important for other reasons.

What you need to check is the characteristic of the fuse and circuit breaker being used. The fuse may be a one time instantaneous fuse, while the breaker is an inverse time unit. The breaker, if so, will withstand the overcurrent or fault current, for a few cycles more than the fuse will withstand either event.

Simply put, a coordination study is needed to determine the type of fault event, and match the overcurrent/short circuit devices to the each other and the load.

Keep in mind that protection devices handle overcurrent and fault currents differently.