How much time do INS1-E and MIN6 cells need after splitting?
Searching literature to see what the published protocols were is the best bet. I found a simple document for INS-1 cells here. There is also this paper describing the isolation of an Ins-1-derived cell line 832/13 which my lab (though not me personally) have experience with. Cells should only be sub-cultured when nearly or fully confluent. With Ins-1 cells that would be a sub-culture ratio of 1:4 to 1:8 and will take 2-3 days. Something to note is that Ins-1 cells are poorly adherent to tissue culture plastic. That's a normal part of their characterization. I remember lab members having to take special precautions with respect to media ingredients to prevent them from detaching, as well as really delicately adding media to the dishes otherwise the force from pipetting too quickly will dislodge many cells and explain why your cells are washing away.