- ♫ The guards are alerted with the sound of magic ♫

Staying quiet is SUPER IMPORTANT until it's not.

In most games I've played that allow fast travel, the lore implication is that your character is actually making the journey to that location in some manual way, and is not teleporting. It's just you, the player, doesn't have to experience it first hand.

In some ways, immersion is adhered to, such as by having in-game time pass.

In another way, you can be completely trapped somewhere with no way to get free and just fast travel to safety so long as you're outdoors with no enemies nearby.

Honestly, I just always think of it as teleportation, much like I consider loading a previous save to be time travel.