I can't locate the installation instructions for that particular model, but it does appear that the gasket is intended to go underneath the pan. If the manufacturer has a recommendation, I'd obviously use that. If that's the case, I'd go with plumbers putty as opposed to butyl caulk for a couple reasons.
First, butyl caulk isn't particularly dimensionally stable - that is, it will have a tendency to shrink over time. Second, it is incredibly difficult to clean up. That means if lay you down a bead of butyl and then clamp the the flange over it you will force some out onto the floor of the pan (and if you don't, you didn't put enough on).
What you'd likely end up with is a mess that you might not be able to clean up without damaging the finish on pan itself with the solvents you'd need to get the stuff off. Silicone, on the other hand, will generally just peel away or come off with light friction (like rubbing it really hard with your thumb), and plumber's putty doesn't really "stick" so it's the easiest to clean up after.
Finally, the last reason I'd steer away from butyl is that it usually takes a long time to fully cure (the last one I used was labelled as 7 days to a full set). This is fine in a gutter where you don't have people walking on it, but probably less so in a shower unless you're willing to sit it out.
Plumber's putty is specifically made for this type of application, and it's so cheap that it really doesn't make a lot of sense to go through the potential hassle to avoid spending a dollar or two just to use up a tube of butyl that you have lying around. The gasket on bottom is doing the majority of the work anyway - about all the seal on the top does is stop water from standing inside the cutout on top of the gasket.