Binance has issued an official announcement regarding the phishing SMS messages shortly after I received the second SMS. It seems that things have calmed down for the time being.
Seems like scammers are still trying as earlier today I got the message that says "You logged in from a new device in Bucharest (Romania) and if it wasn't you, call us immediatelyl at xyz etc". 
It is a very obvious scam attempt but I can imagine bunch of people actually falling for it as it looks like Binance actually sent you a message.