the off-contact shouldn't have anything to do with this problem. Having off-contact too high will cause registration problems though. try to make sure your off-contact is the same for each screen and not very high. 1/8" from the substrate is recommended. you want just enough so that the screen isn't laying on the substrate, but also high enough so that the screen can "bounce" back off the shirt when pressing. having a coin taped to the top of the screen can help with the pop/bounce effect too. Having high tension screens helps too, but we can't have everything 
You need to "flash" the white longer. Remember that White reflects heat/light so it takes longer to flash/cure than other colors. If you are flashing at the correct temp/time then you shouldn't be getting any white transfer on the next screen or screens. You want the ink to be dry, but not cured. Best way to describe it is to have the ink feel sticky/tacky, but you shouldn't have any ink on your finger when touching it. For most inks I think you want to be between 240F and 260F for flashing.
are you letting the shirt/platen cool down before bringing down the next screen?
Also be sure to not cure the white while flashing. If you do that the next ink colors might not adhere well and might fall off or flake during washing.
You need to "flash" the white longer. Remember that White reflects heat/light so it takes longer to flash/cure than other colors. If you are flashing at the correct temp/time then you shouldn't be getting any white transfer on the next screen or screens. You want the ink to be dry, but not cured. Best way to describe it is to have the ink feel sticky/tacky, but you shouldn't have any ink on your finger when touching it. For most inks I think you want to be between 240F and 260F for flashing.
are you letting the shirt/platen cool down before bringing down the next screen?
Also be sure to not cure the white while flashing. If you do that the next ink colors might not adhere well and might fall off or flake during washing.
