Inverted sentences

'Rarely' counts as negative, like 'scarcely', 'hardly', 'seldom', 'only a few', and n-word negatives like 'never', 'nowhere' etc. When these are at the front, the subject and auxiliary are inverted.

Only after my explanation was he able to understand the rule.
Only then did he realize what had happened.

Barely/hardly/scarcely are used to indicate that one thing happened very soon after another.

Barely/Hardly/Scarcely had I seen him, when he ran away.

I barely saw him a couple of times.
Barely did I see him a couple of times.

Only after my explanation was he able to understand the rule.
Only then did he realize what had happened.

Rarely did the Russians use soft power so well.

Rarely have the Russians used soft power so well.