The language's most basic verb marking is for aspect: -ile marks perfective (which may of course overlap with past tense meanings). If not perfective then the default verb ending in -a occurs, which is prototypically present.
There is also an anterior (hence "tense") marker kade (which no one noticed before, but which I believe to be grammaticalized for the most proficient speakers who use the pidgin regularly).
Thus kade idli-ile [ANT eat-PFV] 'had eaten' = PLUPERFECT.
Kade idla 'was eating' (PROG) or 'used to eat' (HAB.PST) does not have a perfective meaning.
The language marks future (which I've always thought of as tense, since there are no other modal verbs or auxiliaries; but I'm not averse to considering zo as a modal.) Hence zo idala 'will eat' (FUT); zo idl-ile (FUT + PRF) 'will have eaten' = rare but attested.
So I now think the best analysis is that the language has (FUT) + ANT + PFV as its basic template.
All three can be combined but
I've not come across an idiomatic example. My informant thinks that zo kade idlile 'will have had eaten' is okay given a particular context (and preceding irrealis temporal clause).