After a bit of testing, tentatively answering own question - yes, it would appear that a prismatic glyph freshly triggered by Hail launched from back bar puts any sort of prismatic damage on cooldown, so swapping bars and attacking can't immediately proc prismatic enchant on main hand of front bar's DW. So: Hail -> bar swap -> Flurry results in just one proc of prismatic enchant if both bow and axe are prismatic, but replacing axe with poison enchant results in prismatic and poison procs appearing almost simultaneously (prismatic from first tick of Hail, poison from Flurry).

Further (and I'm yet to give it a bit more testing), if, after bar-swap, Flurry triggered prismatic glyph on non-infused axe before first tick of the Hail have hit the ground, the ongoing Hail from back bar cannot proc prismatic backbar enchant for full duration of front bar cooldown (4 seconds). So, it appears that putting same glyphs on infused backbar and non-infused front would reduce the damage even more, since front bar procs will introduce longer cooldowns (and weaker procs) while DoT from infused back bar could otherwise proc its own enchant more often.

@ZOS_GinaBruno , no pressure with response time, but would be interesting to hear if this is how it's intended to work (since I only have empirical data).