Must + present perfect in a narration about past events

As far as I understand, the construction must + present perfect is used to make presumptions about past events with the connection to the present:

Look, somebody must've been here - the stove is still warm.

But what about narration which is put in past simple? Can I use the same construction like this:

When I woke up and cast a glance on the ceiling, it must have been the early morning.

Is it correct?

I have just come across this with a language student; they had just covered the rule that you cannot use "must" in the past, then we came across "I must have forgotten to water the plants". I had to find an explanation to this dilemma and it highlights the importance of teaching in context.

• "Must" in case one is used for obligation: "I must wear a uniform" and you cannot construct the sentence with the past simple, here you would substitute "must" for "had to"

• "Must" in case two is used to express a presumption about the past and uses the present perfect and conveys a past action that relates to the present or a later past event in narratives.