Present tense in the narrative past tense

In your example

Alice walked carefully along the uneven lawn, making sure to keep her ankle straight.

there is only one verb marked for tense, i.e. establishing when something occurred relative to the time of utterance, and that is the finite verb agreeing with the subject: walked.

The participle making is present in form, but does not itself have tense. A present participle can be used with a finite verb in any tense, indicating that the action/state described by the participle takes place at the same time.

Next year I’ll visit all the major museums in Rome, making sure I have at least three days for the Vatican. [Future]

Hold the board in place, making sure it's perfectly flat. [Present]

A perfect participle indicates a prior action/state relative to the finite verb:

Having first made sure his shirts were properly ironed and folded, John got down to the business of packing.

Both those two statements are correct, as you're using a participle to add information without using "and" to attach a clause to your sentence. It's somewhat of a grammatical shortcut, but it also adds more of an action affect to the writing, rather than having it seem like a simple retelling of events. This is often used in writing to make the reader feel as if a story in passed tense is happening right before them.

Such as the sentence, "Mia teetered over the chasm, straining and reaching for the dagger that balanced precariously on the ledge not three feet from her."

As opposed to, "Mia teetered over the chasm, and strained and reached for the dagger that balance precariously on the ledge not three feet from her".

Now, there are other ways to phrase that sentence, and what you do depends on personal style, but it is a grammatically correct way of describing a series of actions.