When using with any DAW other than Cubase, you need to use the supplied dspMixFx mixer utility. Is this open? What are your settings - particularly with regard to Alternate or Independent Mode. Is channel linking turned off for the inputs?
I must confess, I use the UR28M primarily with Cubase, but have used it in Standalone mode, but never in conjunction with Logic or any other DAW. Another in the Studio uses it exclusively with ProTools.
The more info you provide the fewer questions need to be asked in order to resolve your problem.
From what you describe you are apparently trying to use an external effect on an existing recorded track - pretty standard technique - should present no problems. I’ve taken all six outputs and routed them to an analog mixer (for OTB mixing and processing) then routed into four subgroups of the mixer connected to the URs Inputs. So I know this works, however I think you’re going to have to be in Independent mode.
Using Mix 1/2 for Monitoring is fine and should present no problems (though I wouldn’t personally recommend it - for other reasons).