Hmmm. Lots of folks looked, but no one had replied, so figured there was no interest.
Thanks for asking.
It is complex.
First, there is no trans problem. This is normal power train-drive train behavior on this car.
Indeed, as counterintuitive as it may seem, the input shaft does briefly speed up - just before being abruptly halted, since the car is stopped for the shift.
It is a real-time race condition playing out inside the different computers. Multiple events are playing out in parallel, very fast.
Both the ECU and TCM are separately and independently seeing and acting upon similar and different asynchronous signals, some of which are high-frequency reporters.
The ECU sees the TRS and knows he has to increase RPM for the impending shift change and load on the engine, but the TCM sees the TRS and knows the trans is stopped.
Meanwhile, the ECU is seeing and processing - and converting - the crank signal. But, the TCM does not see this directly. It gets a converted (PWM) signal from the ECU, after the fact. Kinda like seeing the sun as it looked seconds ago.
Meanwhile, the TCM is seeing the high-frequency-reporting (input shaft) pulse gen signal, which the ECU does not see. And, the TCM sees this directly. So, the TCM knows what is happening to the input shaft, slightly before the ECU's (delayed) converted crank signal (for the torque converter) arrives.
Meanwhile, the TCM has activated the valve body's solenoids seeing its version of the TRS signals, and the hydraulics are unfolding within the trans. And, importantly, shifts into D and 2 and L take longer than shifts into R, because there is a pressure build-up for the kickdown servo's activation for these. This trans and TCM take a two-step sequence to entering D and 2 and L when stopped, which is part of what is called creep. But, there are actually two creep states. (I have another post on that - if anyone wants to help on that.) Anyway, the trans and TCM take a one-step sequence for R, where there also is creep, but not with different creep states (unlike the forward gear shifted positions).
Thus, there is slightly more time for the inversion to play out shifting into D and 2 and L, than R.
So, the ECU commands more fuel for the shift load for D - there is minimal load in P (no clutches nor brakes are applied), thereby increasing the TC's speed causing the impeller to drive the turbine faster driving the input shaft faster mere moments before and while the trans is taking action to stop the input shaft's rotation - which it does, since the car is at a stop for the shift.
And, after commanding the VB's shift solenoids, the TCM grabs its input shaft pulse gen status (which it had to convert) and then grabs the delayed arriving ECU's converted crank signal - where the engine speed already has changed, and then the TCM places these values into the OBD-II protocol message and sends them to the scanner, which does as he's told: displays the un-aligned engine and input shaft speeds.
Thus, there is no actual inversion. It is an illusion, explained by the real-time computers, trying - as best they can - to keep up with the real-time rapidly-unfolding events … which are not waiting on the computers to keep pace/catch up.
P.S. There's actually more to this - with some fascinating corollaries, when they get thought through, including the layout of the gear shift lever positions (P/R/N/D/2/L) and the inverse situation shifting from D to P … and 2 to P … and L to P … and R to P.
By the way, I am finishing writing my second book on these cars. The first is already in the AACA Library and Research Center, thanks to Matt Hocker.