They did not pronounce “La Ilaha Illa Allah” and just did rituals of worship (Salat, Hajj, Siam, Zakat) and then went back to the system of their forefathers as they were doing before in their daily life. No, they did not. That was not Islam for them. They did follow every system their messenger taught them.
What do you think these Muslims should be called today? I’ll let you think, but meanwhile I propose the name ‘Mushrik Muslim’ (though Mushrik cannot be associated with ‘Muslim’, but what can I do? Someone please think of an appropriate name).