Cum soror patrem ad portum secuta esset, praefectum nautis imperantem vidit.

Here cum introduces a subordinate clause meaning something like when or after in a narrative setting.

It is not the preposition cum meaning with. You can tell because it is followed by a full clause, soror patrem ad portum secuta esset, not by an ablative noun.

In narrative Latin, cum often introduces a background or circumstance clause and regularly takes the subjunctive. This is very common in prose.

So cum soror patrem ad portum secuta esset means the circumstance in which the main action happened: when / after the sister had followed her father to the harbor.

Secuta esset is the pluperfect subjunctive of the deponent verb sequor, sequi, secutus sum, meaning follow.

Because sequor is deponent, its perfect-system forms are built with a perfect participle plus a form of sum:

• secuta = participle
• esset = imperfect subjunctive of sum

Even though the form looks passive, the meaning is active: had followed.

Because it agrees with soror, which is feminine singular.

The participle secuta must match the subject in gender, number, and case:

• feminine
• singular
• nominative

If the subject were masculine, you would expect secutus instead.

Patrem is the direct object of secuta esset.

Even though sequor is deponent and has passive-looking forms, it still behaves like an active verb in meaning and can take a direct object. So patrem secuta esset means had followed her father.

Ad portum shows motion toward a place: to the harbor.

This is a very common Latin pattern:

• ad
  • accusative = movement toward

So patrem ad portum secuta esset means she followed her father to the harbor.

Imperantem goes with praefectum.

You can tell by agreement:

• praefectum = masculine singular accusative
• imperantem = masculine singular accusative

So the phrase means the commander commanding..., not the sailors commanding.

Because impero commonly takes the dative of the person who receives the order.

So:

• nautis imperantem = giving orders to the sailors

This is one of those verbs whose object pattern must simply be learned. English uses command someone, but Latin often uses impero alicui.

The present participle shows action happening at the same time as the action of the main verb.

So praefectum nautis imperantem vidit means she saw the commander while he was giving orders to the sailors. The ordering is in progress at the moment she sees him.

Vidit is a perfect-tense main verb, a very common tense for narrating a completed past action: she saw.

The tenses work together like this:

• secuta esset = action already completed before the seeing
• vidit = the main event in the story
• imperantem = action going on at the same time as the seeing

So the timeline is very neat: first she followed her father, then she saw the commander, and at that moment he was giving orders.

Grammatically, cum with the subjunctive can sometimes have a causal sense, and since is possible in some contexts.

But here the most natural sense is temporal or circumstantial: when or after. The clause mainly sets the scene for the main action rather than giving a reason for it.

It is normal Latin word order, even if it feels less natural to an English speaker.

A few typical features are:

• the cum clause comes first to set the background
• the main verb vidit comes at the end
• praefectum nautis imperantem keeps the noun and its participle together

Latin relies much more on endings than on word order, so it can arrange words for emphasis and style more freely than English.