Is the 12-word phrase app-specific?
No your funds would still be at risk. There are only a few popular wallets that use seed phrases.
Most wallets use BIP39(https://en.bitcoin.it/wiki/Seed_phrase) but there are some that use different versions or no seed words at all.
Electrum does not ouse BIP39, see their docs explaining why. https://electrum.readthedocs.io/en/latest/seedphrase.html
It would be extremely easy for an attacker to try the most popular versions and steal your funds.