When adding an inline fuse holder on transfomer it goes on the red wire on secondary side, right?

It definitely goes on the hot side and red probably is hot. What is the other color, White? Then red is correct.

The color is inconsequential. The fuse needs to be in line of the ungrounded hot. If neither of the secondary output is grounded, then does not matter which wire, if one leg is grounded, then install the fuse only in the ungrounded leg.