Some questions about Inversion sentences

Question

Source: https://www.perfect-english-grammar.com/inversion.html

I found this, and it says "We only use inversion when the adverb modifies the whole phrase and not when it modifies the noun."

What does modifies the whole phase mean?

Take the two sentences below for example:

Not until I saw John with my own eyes did I really believe he was safe.

The word "Not" modifies the phase "until I saw John with my own eyes", right?

Only when we had our lunch would we go to work.

The word "Only" modifies the phase "when we had our lunch", right?

What about sentences like below? Is inversion required? Inversion is required only when adverbs like "only", "never", "not".... modify the whole phase, so sentences like below are not the case, right?

When he only eats chips, he gets fat.

When I only do simple things, I can concentrate.

When a man only thinks of himself, he loses his friends.

Answer 1

The words triggering inversion in these cases are not the adjectives themselves, per se, but the negative-polarity words "only" and "not" with the adverbs. If you removed them from any one of the sentences inversion is no longer used:

Until I saw John with my own eyes I believed he was safe.

Since Lucy left college she has had so much fun.

After I'd seen her flat I understood why she wanted to live there.

When we'd all arrived home I felt calm.

By working extremely hard we could afford to eat.

So no, the adverb itself modifying the entire phrase doesn't trigger inversion, the presence of certain negative-polarity adverbs with the main adverb is what triggers the inversion. Other more obviously negative adverbs do this as well: "never", "nowhere", "neither", "nor", etc. All these also trigger inversion when they sit right next to the main verb in their more normal positions as well: Never have I seen..., Nor did he go..., Only with great trepidation did she....