I use my bank APP (BBVA, it seems to be rewarded with the Forrester prize to the best app bank, and it's really good). From this app, I could connect with other banks, to see other accounts (If I'd had). You click in the option, they show a list of banks, and they ask fro you id and pin. Of course, you download a 1mb with terms and conditions.
There's another app here in Spain (I suppose not only here) announced in TV and it's FINTONIC (
https://play.google.com/store/apps/details?id=com.fintonic)
You can read in their website some things they explain about security (
https://www.fintonic.com/es-ES/soporte-ayuda/)
In "Security and Privacy" they say:
"Te registras con tu email habitual y con las claves de acceso de tu banco, son de lectura (con estas claves, ni tú ni nadie podrá operar o mover dinero)."
You register with your email and the access code from your bank, the access code is only-read (with this code, neither you not anybody can make operations or move your money"
They say too they can connect to bank thanks to Eurobits
"Gracias a Eurobits, líder en el sector de agregación de cuentas, los bancos se pueden conectar a Fintonic. Se requieren las claves de acceso de la entidad para agregar las cuentas."