At the shop, we pulled wires from a busway box that is protected with 60 Amp. fuses to wire a single phase 220v machine. The wires were pulled to a 60 Amp disconnect switch box. We also pulled wires to a second circuit breaker panel of the load side (not fuse side) of the machines disconnect box. The second panel will serve the lights, receptacles. The common and the ground of the second panel are run separate to the machine disconnect box. Is this ok?

While wiring a baseboard heater that will be protected by a 30 Amp. breaker in the second box (above) my helper and by mistake connected the in and out on the thermostat with the same hot wire and when we turned on to try the heater, it tripped the breaker which is a good sign that the 30 Amp. breaker worked. My problem is this: Why did the two 60 Amp. fuses at the busduct trip? I am kinda concerned.

Thanks for the help and the directions.
Moe

Generally, fuses operate much faster than circuit breakers due to the inertia of the moving contacts.

I am concerned about your question-
"The common and the ground of the second panel are run separate to the machine disconnect box. Is this ok?"

If you mean that the grounded (neutral) and the equipment grounding conductors are in a different conduit than the hot wires, that is definitely not OK.

Ed