They are in the suggested ranking and full results table, Relic = Relic of Xuen, HLSFO2 = Heroic Lei Shen's Final Orders 2/2, and HDMV2 = Heroic Dark Mist Vortex 2/2. In the OP.

My results:
Simc:
RotFC on mainhand sims 400 dps higher.
RotFC being applied by soul reaper leads to a noticeable increase in uptime, from 74.34% to 76.48%.
Razor ice hits for the same amount on either weapon (835), but is cast more often with razor ice on the mainhand, 497.6 counts versus 466.7. This difference happens to be the exact same numner of soul reapers (31), so we can presume that razor ice change happens because of the lack of SR hits. However, in the sim, this still leads to a net 400 dps loss.

In-game:
Note: Not using log as they seem to not be recording every attack. Recount data will hopefully suffice. Including logs anyway in the hope they show the same trend.
10 minutes on a training dummy, no procs of any kind.

RI in offhand:
Details for Mendenbarr - 19-03 00:41 - Divide - World of Logs
728 melee attacks, 134 miss, 594 melee attacks that actually hit.
291 RI hits

Assuming a perfect ratio of offhand to mainhand attacks, we would expect 297 RI, but whether due to a reporting error or more misses on the offhand, we get 291. Aceptable difference.
RI damage averaged 484.
Tooltip says RI does "2% of weapon damage"
My weapon damage is listed on the weapon as 7334-13623, which averages at 10478.5 damage. 2% of this is 209 damage.
My weapon damage is listed on the character screen as 14025-20313 on the mainhand, and 7012-10157 on the offhand. This averages at 17169 and 8584.5, respectively. 2% of which is 172 and 343 dmg, respectively.
Now, being frost damage, RI is buffed by frost's mastery, which for me is 41.41%, bringing it up to an expected 485 damage, right where it actually is.
Interestingly, RI does not seem to be buffed by RI's debuff on the training dummy.


RI in mainhand:
Details for Mendenbarr - 19-03 00:41 - Divide - World of Logs
758 melee attacks, 149 miss, 609 melee attacks that actually hit.
604 RI hits
This is odd

Assuming a perfect ratio of offhand to mainhand attacks, we would expect 305 RI, we get 302*2. Assuming 302 to 305 is reporting or more misses on mainhand, the number of RI has DOUBLED.
RI damage averaged 485.
Tooltip says RI does "2% of weapon damage"
My weapon damage is still listed on the weapon as 7334-13623, which averages at 10478.5 damage. 2% of this is 209 damage.
My weapon damage is still listed on the character screen as 14025-20313 on the mainhand, and 7012-10157 on the offhand. This averages at 17169 and 8584.5, respectively. 2% of which is 172 and 343 dmg, respectively.
Now, being frost damage, RI is buffed by frost's mastery, which for me is 41.41%, bringing it up to an expected 485 damage, right where it actually is.


Additional data:
RI does not change damage despite swapping to normal rotation, while it procs of every weapon based ability, it remains 485 on average.
RI seems to proc once per non-melee weapon based attack regardless of which weapon has the enchant, with the exception of soul reaper, which I was unable to test on the training dummy, but presume it will only proc when it's on the main-hand.

Conclusion:
RI procs on every weapon based hit when the enchant is on the main-hand weapon, but only procs on either mainhand or offhand (not sure which), when RI is on the offhand. This is not reflected accurately in simC, and napkin maths out to be a 566 dps loss.

If you are concerned about this, please go to the following bug report on battle.net, and state "I am experiencing this as well", and anything else you want to add in.
Unexpected RI behavior - Forums - World of Warcraft



Edit: In the mean time, RI on mainhand is ahead by about 100 dps, based of my above napkin math, so I's suggest swapping over to it. Not going to update the OP unless this continues to be an issue for at least a week, I hope it will get fixed before then. You can help by going to the above link.

I'd like to suggest adding IceHUD + OmniCC to your rune section of mods. I personally feel like its the best because it shows you your runes in the default fashion, except in the lower center of your screen. OmniCC adds visible numbers to the runes and gives off a little blink when it's ready to use. IceHUD is also really good just to have an easy way to see track certain buffs you're interested in tracking, your health, targets health, target-of-target health, debuffs applied to the target, target's cast time and things like that. and if you don't like any of that other stuff, you can just disable it all and use only the rune aspect of it. Also, you could add these macro to your macro section (for those who dual wield) These macros make it so that every time you cast frost strike, it uses any blood charges u have to give you runes in much the same fashion as RE does, except you get death runes instead of those pesky unholy runes. The Death Coil macro is just for those few times that you might have to be out of range and you're spamming death coil and you don't want to cap on blood charges. For those who insist on micro managing their blood charges themselves, a very useful macro would be This one allows you to get 2 blood taps in with the same keystroke if you have enough blood charges. This works because Blood Tap is off of the GCD.