Later, srI MadhwAchAryA, srI VallabhAchAryA and srI Krishna ChaithanyA propagated their siddhAnthAs which differed philosophically [*from each other*].
srI MadhwAchAryA didn't even accept the concept of ParamAthma remaining in the jIva as antharyAmi and established that both are quite different. That is dvaitham.
It will be quite difficult to explain in a nutshell the philosophies of srI VallabhAchAryA and srI ChaithanyA. That discussion is not required now. What I wanted to convey is that, all these three [*AchAryAs*], while establishing a philosophical thought, theologically, established a particular deity as 'the only Godhead'.
Even in the Madhwa thought, only Vishnu is the paramAthmA. Krishna alone is Bhraman or paramAthmA, even for the other two [* VallabhA and ChaithanyA*]. Hence, these paths too are based on Vishnu upAsanA. People have migrated even to these sampradhAyams, only from smArthAs. Among those converts, in addition to those who opted for the new path purely based on the philosophy, would there not have been smArtha-vaishnavites, who chose the new path exclusively because, a highest place had been accorded to their favourite [*deity*] Vishnu ?
Summing up, only from the smArtha sect, people had moved later to all the Vaishnava schools such as RamAnuja siddhAntham, Madhwa siddhAntham, Vallabha siddhAntham, Chaithanya sampradhAyam, and (There was one NimbArkar - He was also a Krishna devotee) His siddhAntham.
Therefore, among those who stayed back as smArthAs, the proportion of vishnu devotees would have gradually reduced and wouldn't that of bhakthAs of Ishvara (Siva) have increased [*in due course*]? That is why the popular notion that advaitins are saivaites had gained currency!