combined probability of causally-linked events: joint probability?

That's correct.

If the population is 100,000 and 1.2% contract the disease, that means 1,200 get the disease. If 1.8% of those who get the disease die from it, then .018 x 1,200 = 21.6 die from the disease. 21.6 / 100,000 = .000216 = .0216%.

Causality isn't really relevant here, only conditionality. You could just as easily ask what is the probability of rolling a 6 on one six sided die, followed by either a 3 or 5 on a second six sided die. There are 1/6 ways of rolling a 6; and there are 2/6 = 1/3 ways to roll either a 3 or a 5. 1/6 x 1/3 = 1/18.

The key to calculating probability correctly is always the same, though the exact method will differ:

(1) Figure out the total number of ways an event can occur

(2) Figure out the total number of ways the desired event can occur

(3) Divide (1) into (2) to get the probability.

For example, in the case of the dice rolls, there are 6 ways to roll the first die, and 6 ways to roll the second die, so the answer to (1) is 6 x 6 = 36.

You can roll a 6 followed by a 3, or a 6 followed by a 5, for the desired event. So the answer to (2) is 2.

Then the answer to (3) is 2 / 36 = 1/18.

Applying this to your original problem, if we set the population at 100,000 then each lifespan is an event, so the answer to (1) is 100,000. The number of "desired" events is 21.6 as calculated from this above. Then the answer to (3) is 21.6 / 100,000 = .000216 = .0216%.

When the total number of "events" is not problem dependent, you can substitute any convenient arbitrary figure for (1).