It will be interesting to see what driving conditions trigger the engine drive mode as the engine will be Atkinson cycle and therefore relatively low torque at lower speeds (but the motor is available at any time to provide a torque boost). Perhaps cruising at 35 mph with the engine at a bit over 1000 rpm? This would mean the engine running at around 2000 rpm at 60 mph which is similar to the current CVT gearing.
To be technically precise, we have to call I-MMD the Honda system and HSD the Toyota system, and they both are E-CVT.
There will be many parameters for triggering; vehicle speed, rpm, state of charge, gas pedal pressure, air conditioning request (cooling or heating), slope, cooling temperatures (petrol engine, battery, inverter and electric motorgenerators), and maybe the ECU could have an adaptive software, so triggering points could change for each driver.
As for Toyotas, the aim for this kind of hybrids is the highest efficiency, this means keeping the petrol engine in the best working conditions. We know that traditional engines, coupled with standard transmissions (manual, cvt, converter) are set to have a medium efficiency in all working conditions, from idle to max revs, for each gas pressure, this to ensure a good driveability and low emissions both for low speed and for high torque requests; engineers work to rise the medium efficiency, because they cannot sell an engine with a 6 gear transmission that works very well at 2000rpm with 1/5 of gas and rattles at 2200 rpm with a 2/3 of gas pressure. But they can sell an engine that works very well in some conditions and very bad in others with a system that keeps the engine only in the best and avoids it running badly, for instance avoiding to run with the throttle valve at less than 50% opening: under that value, the engine is switched off, because of pumping losses. For instance, avoiding frequent rpm and torque variations, so the system will keep the engine as stable as possible, and will regulate the power request to wheels using the electric side: if the petrol engine gives 30hp but the driver needs 40, the other 10 will arrive from the battery, and if the driver wants 25hp five seconds after, the surplus 5hp will be sent to the battery.
At cruising speed the I-MMD prefers to close the clutch because the whole system efficiency (petrol engine plus transmission) is higher; the petrol engine runs in medium rpm, throttle valve well opened (surely the i-vtec will set an high livc, late intake valve closing, and this will regulate the power limiting pump losses), and in this conditions it's better to feed the wheels using a direct shaft than a double energy conversion (mechanical to electric, regulation, electric to mechanical), leaving this at lower speeds and when power request changes frequently.
Toyota use another system with the petrol engine always connected to wheels using a sort of differential called PSD, power split device; this pattern was patented in 1972 in the USA, power from petrol engine is sent to this asymmetrical differential, about 70% goes to wheels, 30% goes to another electric motor-generator used to regulate the whole system, because this electric machine can be used as generator or a motor to raise or reduce ICE rpms.
http://eahart.com/prius/psd/Toyota used this pattern to have smaller and lighter electric motors, best for system efficiency but worst for power response, I-mmd is definetly more powerful and fast responsive.
https://www.caranddriver.com/reviews/comparison-test/a28316198/2019-honda-insight-vs-2020-toyota-corolla-hybrid/