This isn't formally specified on Ocean's panel because it's virtually never relevant with just the core game, and spelling it out would both take up a lot of space and needlessly increase complexity / confusion-potential for players who only have the base game. However, it becomes very relevant when playing vs. The Habsburg Monarchy Lvl 4+ (Jagged Earth), which blunts "Destroy Town" effects; see
this FAQ if you need details.
The fact that the Push is part of the triggered action means that it can trigger further actions – e.g., Melt Earth Into Quicksand or Call to Guard in the land Pushed to – which cleaning up illegally placed pieces does not do.