Now, that is what aI would call inexact science. qsowhere in the range of 10,000 to 2,000,000 years ago. Yes, that pins it down for me.
You seem to be having trouble grasping the nuances of dating systems.
Let me take a stab at explaining it to you.
katyusha states: migrated northwards during the Pleistocene (approximately 2 million to 10,000 years ago)
The 'Pleistocene' is a name given the time period from 1.8 million years ago to 12,000 years ago. This is a named time period in the same sense that the month of August is a time period.
Many things can occur in that time period. Just as you (or others) go to work 22 times or so in August, just as you go shopping in the month of August, just as you may go on vacation in the month of August, during the Pleistocene, glacial and interglacial periods mark the advance and retreat of large glaciers in the Northern hemisphere. During each of those glacial periods, Mammoths, or their immediate ancestors, migrated south. During the interglacial periods, those periods where the glaciers retreated, the mammoths, or their ancestors, migrated North.
You can see from this that there is no 1,900,000 year uncertainty in the dating as your post suggests.
I hope this clears up any misunderstanding you have about named time periods and Mammoth migration.