This is browser version related issue.
It occurs only on the latest version of Firefox (57.0.4 - Quantum).
Time picker can be interacted with, but when any of the time picker fields is selected - the options drop-down doesn't open.
If the time picker field is clicked on repeatedly, it can be seen that the options drop-down gets open, but only for a split second.
Attached screenshot shows the expected behavior, taken using Chrome browser (Version 63.0).
Time picker on Firefox 52 (the latest ESR) also works as expected.