With a modal verb such as moeten, kunnen, willen or zullen, the separable verb goes to the end of the sentence as one full infinitive. The separator that normally splits in a main clause stays attached, and “niet” is placed directly before that full infinitive, or before the phrase it actually negates.
For your examples: “Tommy staat om acht uur op” becomes “Tommy moet om acht uur opstaan.” The negated version, if you mean he should not get up, is “Tommy moet om acht uur niet opstaan.” If you mean he does not have to get up, use “hoeven”: “Tommy hoeft om acht uur niet op te staan.” This is an important distinction, because “moet niet” often sounds like “must not,” while “hoeft niet” is the normal way to say “does not have to.”
Similarly, “Johan komt om drie uur in Amsterdam aan” becomes “Johan moet om drie uur in Amsterdam aankomen.” For a negation that removes the obligation, say “Johan hoeft om drie uur niet in Amsterdam aan te komen.” If you put “niet” right before “om drie uur,” the meaning changes: “Johan moet om drie uur niet in Amsterdam aankomen” suggests it is not at three o’clock that he has to arrive, but at some other time.
Why does this happen? A regular main clause splits a separable verb: “opstaan” becomes “sta ... op,” and “aankomen” becomes “kom ... aan.” When you add a modal verb, the modal is the finite verb in second position, so the separable verb no longer needs to split. The full infinitive sits at the end: “opstaan,” “aankomen.” With verbs that take “te,” such as “hoeven” or “proberen,” the “te” is inserted inside the separable infinitive: “op te staan,” “aan te komen.”
A practical next step is to take the separable verbs from your course handout and make pairs. Write one sentence with the verb split, then a second sentence with a modal and the full infinitive at the end. Add one positive and one negated version. This will train you to see “niet” as a marker that goes before the infinitive, not inside it. When in doubt, use “hoeven” for negative necessity and reserve “niet + moeten” for rules and prohibitions. This distinction is one of the most useful habits for natural-sounding Dutch.