I've no time now to investigate further, but I'm guessing you have One Of These 415v output converters.
I struggle a bit with their product information since they moved over to ebay only sales info.
However, from that ebay shop;
PLUG & PLAY MODE
Another SPECIAL feature of this converter is the ability to run it in Plug and Play mode,
In this mode you can take the 415 Volts output of the converter and connect it to your machine so that the existing machines START/STOP buttons and switches will still work to control the machine as if it was connected to a factory 3 phase supply,
You need to take into account the motors starting requirements when sizing up the converter for Plug and Play mode, normally a 3 phase motor will require at start up a surge of 3 to 8 times the normal running power and the size of converter needs to be large enough to provide this power,
Unless the machine has a very high start load for example in the case of a planer machine because of the cutter block's inertia you can go for a 3 x overload rating, as an example the main spindle motor on a 2HP Bridgeport Mill will require a 6HP surge to get it going,
All this range of DIGITAL Plug and Play Converter allow you to take a 150% overload for 30 seconds so the 6HP starting requirement of the 2HP mill can be accommodated by this 5 HP converter,
As the output from this unit is a DIGITAL output you can only use it to power normal motor/switch loads and not any items that contain electronics,
If you need to provide power for an item with electronics of any type you will need to fit a SINE WAVE FILTER(See ) to the output, once you have this fitted then you can power machines with electronics in them and even running a CNC machines is possible,
Hence it seems that when used in your current Plug & Play mode, downstream switching is OK, but you need to take starting surge into account.
I'm sure it's quite a sophisticated unit, which can also be programmed as a normal single machine inverter, but does have the extra facility to connect directly to a standard 3 phase machines input, albeit at a price.
I'm guessing that most folks on these have little experience of one of these inverters, but the vendor claims to offer telephone support.
Bill