Learn Russian: Если ты менеджер, то ты должен управлять ситуацией. - If you are a manager, then you must control the situation.

The verb управлять (to manage, control, or steer) always requires its object to be in the Instrumental case. This is a common pattern for verbs dealing with leadership, management, or control, similar to руководить (to lead or direct).

What is the purpose of то in this sentence? Doesn't it usually mean "that"?

In this sentence, то means "then". It acts as the second half of the если ..., то ... (if ..., then ...) structure. While English often skips the word "then" in "if" sentences, Russian strongly prefers including то to connect the two clauses.

Должен means "must", but why does it behave like an adjective instead of a verb?

That is because должен is a short-form adjective. Instead of conjugating like a normal verb, it changes based on the gender and number of the subject. Here it is masculine, assuming ты refers to a male. If addressing a female, you would say ты должна.

I have learned that professions sometimes take the Instrumental case. Why is менеджер in the Nominative case here?

In present-tense sentences where you say "Subject is [Profession]", the profession stays in the Nominative case because the "to be" verb is omitted. You only use the Instrumental case for professions in the past or future tenses (for example, ты был менеджером - you were a manager).