Tower Aggro or Attack Priority?

So I've played a few games where I'll create a minion rush towards a tower in the early game. Then I run up to the tower under protection of the minions and wail at it.

But then, out of nowhere, the tower begins targetting me, usually after an attack. Why? I thought towers prioritized minions?

In addition, sometimes an ally champion is being hit by the tower, I'll attack the tower, and it suddenly starts hitting me. Oftentimes, these are at precisely the times I am lower on health, so it is frustrating, and I cannot find documentation on this mechanic.

For example: http://leagueoflegends.wikia.com/wiki/Turret

• Attacks pets, then super/siege minions, then minions, then champions.

This explanation differs from what I've seen in matches... Does anyone know the true mechanics?