InDesign does use ‘true’ ligatures – of course only when they are provided in the font to begin with, and it also has to ‘know’ that they are there (i.e., the ligatures are properly indicated with one of the OpenType features).
Your test with Times shows that this is most likely not a proper OpenType font and so it doesn’t contain any other ligatures than “fi” and “fl”. These two are special in that they pre-date OpenType; they are ‘normal’ characters, but InDesign is smart enough to find and use them anyway.
The reason that Dwayne believes that InDesign fakes ligatures: “… two characters. InDesign just makes them look like ligatures …” is also because InDesign is way, way smarter than your Average DTP software. It scans regular text strings for combinations that can be replaced with ligatures, and when it finds any, it does not change the text but only the display. This is why you can search for a single ‘f’ and it finds this even when in a ligature, and why you can place the cursor ‘between’ two characters ‘inside’ a ligature and type a single letter which seemingly automatically ‘discards’ it.
… Back to the original question.
> For example, I am using FF Tisa Pro which has ligatures for ch/ck/ct, but they don’t appear normally.
.. which is actually a good thing :) The common ligatures “fi” and “fl”, and in some fonts combo’s such as “ff”, “ffi”, “fj”, “fk”, “ft”, “fh”, and “Th”, are designed to prevent optical clashes between the overhanging part of the “f” and the next character. Some fonts don’t need a ligature because its design makes it unnecessary; then again, they still may contain a design for the standard ligatures because a text file may contain these character codes.
The design for the ligatures you want is beyond this common use, and so they have an OpenType feature of their own: “Discretionary Ligatures”. As with all OpenType features, the character designs must be in the font and the correct OpenType feature must have been inserted as well, for InDesign to be able to use it.
This seems to work for FF Tisa Pro: see https://myfonts.us/td-M6bEf4; I ticked the box “Discretionary ligatures” in the Typographic Variant settings, and lo, it contains both ‘ct’ and ‘st’.