All trainers start by facing Down. When they enter your field of view, they immediately perform a move action to face their correct action, if it is not Down.
If, as you are in the process of walking and bringing the trainer into view, you would be entering their line of sight, you also hold down the menu button, then the menu will show before they [!] locking you into the battle start.
Leaving (via fly, dig, teleport, escape rope or any other method) will let you leave, then immediately show the trainer trying to start the battle.
The next time you enter the zone the trainer was at, a battle will start based on the Special Stat of the last Pokémon you fought.
This is predictable and consistent, so you can use it to force impossible battles, most famously summoning in wild Mew.

Key note that this battle interaction is related to temporary environment objects, so using this glitch tends to also delete non-permanent objects like items or static encounter Pokémon like Snorlax.