One-hot machine transition table
Karnaugh don't work here this way

It works, you just didnt plug the Don`t-care terms. In the k-map drawn; you assumed that when the inputs are 1010 or 0100 the output = 1, while any other value the output is forced to be equal to zero, but in fact none of the other values can exist in your FSM you need to use them as dont cares in order to reach the minimized form of your equation.
Using My python script here are two different scenarios
Scenario 1: i didn't provide the don`t care terms

Scenario 2: Added the don`t care terms

Both equations are true, but one of them is implemented with more number of transistors than the other, so you should always include the don`t care terms [if exisit] inside the K-map in order to reach the minimum form