Mob farms do not work right on realms. i.e. my gold farm on my realm only spawns a few pigmen, and their agro doesn't last more than a few minutes at least. But on one of my single player worlds, it works perfectly. Other people have had the problem too, and were asking about it in the comments of the youtube tutorial I built it from.

Same thing with other farms, not very many mobs spawn, and the realm is on hard.

https://www.youtube.com/watch?v=l9oteFEj770&t=

^^Above mentioned video