I am wondering if the original fuse was replaced when they added the extra load.
Maybe but I took a look at an identical starter minus the interlock and it has the same size fuse. Here is an image of that identical starter (Cutler-Hammer 9586H6045G Model 6-1-3 contactor):
For comparison I metered the current on the secondary of this starter - 0.4 amps.
That starter is 1960's vintage, sometimes in the early 1970's C-H replaced that style with the now obsolete Citation series starters & contactors.