Some dim and distant recollections from the A109AII:
The inverters were an issue inasmuch as if you left them off until after engine start and gens online, it took a while for the AC systems to get up and running so IFR checks couldn't be done until they were
BUT if you had a soft battery, running the inverters before first start could leave the start at risk of going hot.
Delaying turning the gen on after start (optimum one minute) is common across C20 applications, be it SE or multi. The starter gen is just that, both a starter and a generator; so it pays to let the poor thing settle down before switching from one mode to another. Shearing the quill is usually the result, to the chagrin of many a hotshot getting airborne too quickly in a Bell 206!
The engine oil temp would suffer from poor cooling airflow in protracted hovers, even worse in the A109C with the coolers buried into the airframe. They need forward airflow to keep cool.
ISTR that after start, 70%N1 would be selected for idle having checked that ground idle was 61 +/- 2%. We didn't idle for any protracted period at ground idle.
I believe that MOSTAFA is referring to the A109A, which had only two inverters and a significantly different electrical system. The AII was totally redesigned and a third inverter was part of that, as was the hydraulic system.
I'm riding home (leaving tomorrow) and will check my memory against the flight manual in the study when I get there!
edit: I see in your photos that the triple tach is down one engine, and the Nr is set too high?