Order of samples for RNA extraction
What you do not want to do is prep all your control samples on one day, and all your treated samples on another day, because you will not be able to separate differences caused by treatment from differences caused by batch effect.  I'd worry more about that than from cross contamination.  Since you probably aren't comparing the different tissues to each other, batch effect between tissues won't be much of a problem.  So do all your spleen samples, treated and untreated, on one day, all your kidney samples the next, etc.