JavaScript (ES7), 84 bytes

n=>{a=[];for(i=n**n;j=i--;j||a.unshift(i))for(b=0;(b^=f=1<<j%n)&f;j=j/n|0);return a}

JavaScript (ES7), 86 bytes

n=>{a=[];for(i=n**n;i--;j||a.unshift(i))for(j=i,b=0;(b^=f=1<<j%n)&f;j=j/n|0);return a}

JavaScript (ES7), 68 bytes

n=>[...Array(n**n).keys()].filter(i=>!/(.).*\1/.test(i.toString(n)))

Note: This fails with a RangeError for n > 9. 78 bytes handles n up to 13, after which the code falls into an infinite loop due to floating-point precision:

n=>{a=[];for(i=n**n;i--;)/(.).*\1/.test(i.toString(n))||a.unshift(i);return a}

JavaScript (ES7), 84 bytes

n=>{a=[];for(i=n**n;j=i--;j||a.unshift(i))for(b=0;(b^=f=1<<j%n)&f;j=j/n|0);return a}