How can I be sure that device executes the code posted on github, not a different one?

You can verify the integrity of the software running on your device. As in their ledger blue checkGenuine.py (https://github.com/LedgerHQ/blue-loader-python/blob/master/ledgerblue/checkGenuine.py#L72).
Basically you are using:

Code:

pip install --no-cache-dir ledgerblue
python -m ledgerblue.checkGenuine --targetId 0x31100002

You find the secp256k1 public key for the current batch here:

Code:

args.issuerKey = "0490f5c9d15a0134bb019d2afd0bf297149738459706e7ac5be4abc350a1f818057224fce12ec9a65de18ec34d6e8c24db927835ea1692b14c32e9836a75dad609"

( https://github.com/LedgerHQ/blue-loader-python/blob/master/ledgerblue/checkGenuine.py#L119)

To go even further you could try to open your ledger and check whether there is an additional chip implemented and the MCU is an stm2f042k6 (with 32 Kb flash, as a bigger flash could contain code fooling the Secure Element validation). Ledger has described this pretty comprehensibly here: https://ledger.zendesk.com/hc/en-us/articles/115005321449-How-to-verify-the-security-integrity-of-my-Nano-S-