Grid synchronizing is not the same as being able to operate in island mode. The only reason you can run those inverters without an automatic transfer switch is because they don't function when there's no grid to follow so they shut off when power goes out meaning they don't backfeed the grid outside the home.

A lot of inverters are just grid following and you need some other source creating the 60-hz signal for the solar inverters to follow. Generally this is either a battery or generator because solar has a really hard fall off in the power provided the instant you try to draw too much so instantaneous spike loads like motors starting (compressors/fans/etc) will often collapse off grid solar only installs.