What do we call the spike in the cap of an ointment/cream tube?

Solution 1:

Spike, as you suggested, is a pretty clear term. Here is one source about eye ointment that uses this word:

Many tubes have a metal skin on the opening that must be pierced using the spike on the lid of the tube.

Here’s another source about Fucidine Ointment:

Then push the spike in the cap through the seal on the tube.

Solution 2:

The one tube I have handy says:

To Open: Remove cap, flip, and puncture safety seal.

So its completely possible to instruct in the use of the feature without having to name it directly. For example, one doesn't need to name the threads to describe "unscrewing the cap."