This is for current generation NFC chips, the next generation are a bit more flexible:
From the NFC chips point of view, the chip has two different hosts, the Secure Element and the Android host.
The NFC chip also knows which host has opened which operation mode on the NFC chip (e.g. peer-to-peer, reader-modes, card emulation modes etc).
Requests and events that belong to one operation mode will only be send to the host that has opened the operation mode.
For secure elements the most usual 'mobile payment' configuration is that the SE opens card emulation in the NFC chip, and the android hosts opens reader-modes and peer-to-peer.
If an external reader gets detected by the NFC chip all communication will get sent to the SE only. The Android host will not see any of the data exchanged between the SE and the external reader. The android host may however see that an external RF field has been detected at the antenna, so android knows that something is happening.
The software running on the SE usually consists of a small OS that manages multiple applications, parses the SELECT AID command and forwards the requests to whatever application matches with the AID.
The applications running on the SE may decide later to send data to the android host. These events are called transaction events and are a one way communication. The android host is not able to reply to the transaction events sent from the SE.
The android host will also not be able to send data to the SE via the NFC chip. If it wants to communicate with the SE directly, e.g. to install a new application, it has to use another physical connection, usually the sim-card pins or the micro-sd pins.
For completes sake: There are also embedded secure elements that are built into the NFC chip. These don't have any physical connection and the NFC chip allows bidirectional communication between the android host and the SE host.