If Dylan's frequently under the influence he could have made a mistake with the date.
What he saw could have been on a different night.
As to whether he actually saw Tom or Kate that's another matter.
I don't think he's lying about having seen Emily there at some point based on the way the final clip was shown , it was supposed to show the difference between who he had seen picking up Emily and the reality.
Tom is lying if Dylan saw Emily running in the woods that night.