Ah, deimaginators. The supreme scourge of the smuggling society. But they don't have to be! There are many ways to deal with these reptilian pursuers, and as a Glitch who has completed no fewer than eleventy-seven smuggling jobs, my job is to detail each and every one of these methods, from the safest to the boldest -- that way, people of all persuasions can take up this honorable trade. (Okay, maybe it's not honorable, but seriously...they reward you with diamonds!)
Easy
There's never any shame in doing things the easy way. Well, sometimes there is, but not this time! All you have to do is walk slowly. Keep the deimaginator visible on your screen at all times; if you go too far, stop as soon as you can, and he'll most likely shuffle right back into your field of vision. Keep an eye out in both directions though, because if you go too close to normal speed for too long, he may decide to just teleport in front of you. Which brings me to...
Medium
This is the way I usually do it, as the easy way requires a fair amount of patience. Just go on down the street the way you usually would. Once or twice, the deimaginator will appear in front of you, and it will be pretty sudden, but with decent reflexes, all you have to do is jump over him and keep going. If you keep the sound on, you will be able to hear the teleport and know roughly when this will happen. Otherwise...
Hard
The above method is more difficult without the sound on, because as I said, you won't hear the telltale warping sound; he will appear as if out of nowhere. You'll need to keep a sharp eye on the screen at all times.
Expert
Deimaginators? Pfft! Forget them, I've got things to do! If you're really up for a challenge, here's the crazy way to do it. Harvest trees! Go along and pick everything you see. This requires a lot of running back and forth, not to mention jumping; remember, you are frozen in place for a short time when you harvest. Whenever he gets close, run some distance away, wait for him to approach you there, and then jump over him and dart back to the tree. The trick is to make sure he's always too far away to capitalize on your moments of weakness.
(Feel free to throw in animal interactions as well. I don't recommend mining, though, just because of how tedious it will be with all the running and jumping -- remember, rocks can be mined many times each, and they're as stationary as trees.)