Minecraft – How to stop creepers blowing up the Zombie XP farm

There is a safe radius around the player where creatures can not spawn. Normally (depending on how big of a 'trap' you have built) the player's radius includes a dungeon spawning trap. The Dungeon Spawner is unique in that it ignores this normal requirement for spawning, which is why they keep appearing in front of you.

So, if your no-spawn radius includes the dungeon then you are ok. Also of note is that dungeon spawners will spawn creatures in mid-air and above water, normal creatures can not do this because of the spawning rules. Again, depending on the design of your trap it should be inherently safe.

However if wherever you are standing can be reached by just walking or 1 block jumps or multi-block drops, be aware that something can spawn outside of your safety radius and eventually find its way to you. I suggest only going AFK if you are completely sealed off :)

The answer you are looking for is hidden inside you own question: "there are a lot outside". The game randomly checks places to put mobs and since the outside is much larger than your trap, most of the zombie pigmen spawn there. The mob limit is exhausted pretty much instantly and the game doesn't spawn any more, unless some of the existing mobs de-spawn or get killed.

You will get zombie pigmen to spawn in your trap eventually, but you may have to wait hours for just a few spawns. You need to prevent spawning outside your trap to improve rates of your trap. This is very difficult to do in the nether, since you can't use light or water to prevent spawning. That is why you don't see zombie pigmen traps, building one is a monumental project. Notice for example here a huge area is covered with half-slabs to prevent spawning.

The spawnable area is +/- 8 chunks from each chunk where there is a player (minus the chunks on the edges of that area). If a single player is online, mobs spawn in 240x240 blocks area centered on the player chunk, that is roughly +/- 120 blocks from the player.